text:
Collaborative play writing/French chronicles of the 1590s/Act 4

Act 4. Scene 1. At the conference in Suresne. 1593

Enter the dukes of Feria, Mayenne, Guise, and Aumale

Guise. When Frenchmen grumble, peace-time lies amort.

Aumale. Will none agree? While we deliberate,

The Béarnais approaches Paris, glad

Of controversies in religion's camp.

Guise. The Béarnais with England blustering Down many forts and towns.

Aumale. What if they do? We'll fight despite their teeth

Stuck on our bosoms.

Mayenne. We'll grapple with them. But will Spain send arms

To stifle altercation's stirrers-up?

Feria. France sleeps on Spain's religious bosom. Did

My king arise to serve Bartholomew

While sitting to his feast of blood in France?

I think he did.

Mayenne. Can you converse more freely? Will you tell

Of Spain's conditions should she interfere?

Feria. By my faith, very little in exchange

For troops of warriors ready to shoot down

With hunting faces controversy's harts.

There is another fashion to catch them:

Resigned to quiet France in love and hope,

Spain's daughter as your sovereign may be crowned.

Guise. The people disallow her sympathy.

Aumale. My fiery lord of Guise, what if they do?

Seditious mouths are sent in trenches to

Converse with louder cannons nearest foes.

Mayenne. France wishes for a king, no foreign queen

Sufficient for her holy purposes.

Aumale. No doubt.

Feria. Should it depend on us, contentious lords,

Religious Guise is henceforth king of France.

Mayenne. The legate of the pope, my beehive lord

Of stings and sweets, does not agree with you.

Aumale. We all heard him.

Feria. Lords, should we not combine our interests?

Is not my lord of Guise in marriage rites

The readiest to pierce through the right way in?

Guise. I am.

Aumale. Spain mocks the pope and us.

Feria. Who dares pronounce one word against Spain's faith

In Rome's supremacy throughout the world?

Mayenne. The Catholic League.

Aumale. Our Holy Union.

Guise. The Holy Union once obeyed her head:

The duke of Guise my father, dead for her.

Aumale. Our people will revolt against Spain's wish.

Mayenne. Should any even mention barricades,

I'll have him stabbed.

Aumale. I will lend you the poniard.

Mayenne. What will Spain yield to us?

Feria. A glorious troop of forty thousand men

And necessary ecues for your wars.

Guise. With me as king.

Aumale. With death as king.

Mayenne. This may be thought on.

Aumale. Will you turn round with them, Lord Weathercock?

Feria. The Guise is king.

Aumale. That should be seen.

Feria. I'll lie a-groaning in Bastille until

My master's loyalty is known to all.

Mayenne. The duke of Feria's head cannot be weighed

With France's crown.

Guise. What is your wish, my lord of Mayenne? Will

You have the leaves of France quite overrun

And chewed by caterpillars of reform

While we talk in our sleep?

Aumale. My lord of Mayenne wears with his breast-plate

Steel in a baldric sharper than most tongues.

Guise. With Spain his powers thicken on the ground

Like martial-bearing bees do in the air.

Mayenne. Should I invite invaders into France?

Guise. Yes, when the Huguenots encroach within.

Aumale. The English mastiffs mouthing with Bordeaux'.

Mayenne. More on such topics afterwards. Join them,

Lord of Aumale, for some refreshing drinks.

Feria. Refresh us with the blood of Protestants.

Guise. The only cup we long to put our lips

To at this time.

Aumale. Unless I gain with Catholic war-friends

The triumph of our cause, or slide with them

Into the mud of graves, Aumale is sad.

Exeunt Feria, Guise, and Aumale, enter Bévue

Mayenne. Ha, nothing is accomplished when we talk.

Tell me, Bévue, what further news arrive

From Paris, worried by tergiversations?

Bévue. As much as I can tell, too little yet.

Mayenne. Here I am judged, there I judge others. Say:

What matter makes men gabble needlessly?

Bévue. A newborn's murder, committed, we hear, by the mocking donkey's daughter.

Mayenne. I'll see this girl to punish him twice more.

Exeunt Mayenne and Bévue

Act 4. Scene 2. A street in Paris. 1593

Enter Fathers Aubry and Lincestre

Lincestre. Not Father Aubry, celebrated for His fire? We meet.

Aubry. Lincestre, I think, celebrated for his smoke, hiding true dogma.

Lincestre. Lincestre, whom you often speak about aloft in pulpits.

Aubry. Why should I not before some scissor off

The holy puppets of lewd Protestants?

Lincestre. Entirely Catholic, because charitable and loving, with hopes that the king will eventually amend his doctrine.

Aubry. Pray for the Spanish king's daughter as our queen.

Lincestre. No.

Aubry. No?

Lincestre. France never will embrace a foreign one,

Unknown of any, on the bed of peace.

Aubry. Consider the Spanish king's daughter as a female Isaac, sacrificing her body to religion.

Lincestre. No.

Aubry. No?

Lincestre. You are rumored as the king's chaplain and confessor.

Aubry. I? No.

Lincestre. However that may be, I have received

Some letters from the king concerning his

Commands on his conversion at Saint-Denis.

Aubry. The king will not be crowned.

Lincestre. No?

Aubry. No.

Lincestre. Who will forbid it?

Aubry. The Guise is our new David, to lop off

Such monster heads as some in France adore.

Lincestre. That boyish boy?

Aubry. Yes.

Lincestre. Yes?

Aubry. He'll clip your king, to make him nakedly

Bestride the leafless bushes of his church.

Lincestre. He will not.

Aubry. I say he will. Will you creep to Saint-Denis?

Lincestre. To Saint-Denis in an open retinue with the archbishop of Bourges, the bishops of Nantes, Chartres, Mans, Evreux, the curates of Saint-Sulpice, Saint-Eustace, and Saint-Merry.

Aubry. Saint-Merry? I'll have him hurdled naked to the post of infamy.

Lincestre. No.

Aubry. Yes.

Lincestre. However that may be, benedictions on our work!

Aubry. Maledictions on your treasons!

Lincestre. Benedictions on the king's entreprise!

Aubry. Maledictions on your king's hypocrisies!

Lincestre. Benedictions on this homage to religion!

Aubry. Maledictions on religion's desecration!

Enter the archbishop of Bourges

Bourges. What shouts are these? No children but loud priests?

Lincestre. Father Aubry's hopes do not rise with ours on Denis' fertile bed.

Bourges. No?

Aubry. I'll bite before I honor this king as

His majesty.

Bourges. Despite his teeth, we'll crown a Bourbon king

Before the eyes of France and all the world.

Aubry. No.

Lincestre. No?

Bourges. Bite as you will. Saint-Denis for a crown

On top of France, so long without a head!

Exit Bourges

Aubry. Look for the Béarnais to faint and fall.

Lincestre. No.

Aubry. No?

Lincestre. No.

Exit Lincestre and enter Brin carrying shoulders of mutton and veal

Brin. His Spanish majesty's servant thanks your zeal.

Aubry. Ha! Twice more than expected this week. But, Brin, while men watch, you should not stride so openly with the Spanish king's gifts.

Brin. I waited till your angry brothers left.

Aubry. No brothers, Brin, apostates as I say

And always will maintain. Enough of them!

I'm hungry, Brin.

Brin. Then I should be more cherished for the load

I bear alone.

Aubry. A blessed burden! Speedily away

To church and table while the priest is well!

Brin. As fast as drudges bustle, folded twice

More than a man should reasonably be.

Exeunt Aubry and Brin

Act 4. Scene 3. The Bastille in Paris. 1593

Enter Bailleton, Blanchefleur, and Benoît

Bailleton. You'll both at least be hanged.

Blanchefleur. Iron sir, pity my bowels! Say that your judiciary experience may err concerning a young girl's hopes, never before contrary in any fashion to her country's laws.

Bailleton. I do not hope to know so much as that.

Benoît. I swear on her behalf, much more on mine,

Mere innocents before ill-thinking eld.

Bailleton. I cannot tell, except that I believe

Parisian strollers at Grève's public square

Will idly glance on dangling pairs of feet

From soggy bags of piss. Blanchefleur. O, never say so while I live.

Benoît. More miseries, ourselves the source of them!

Bailleton. I cannot tell. With luck or gold, perhaps

You'll merely lose your lives.

Blanchefleur. Our heinous guilt: the burying of a corpse.

Bailleton. Guilt is a word I understand too well.

I'm sorry for your necks and other parts.

Blanchefleur. Who hears the innocent?

Bailleton. Murdering a newborn is a horrible act of crime, I hear. That's all I know, or expect to know, this month.

Blanchefleur. With old suspicion smelling any fault-

Benoît. Youth always hops for it.

Bailleton. Hanging is a kind of groundless meditation, a stationary fall, a downward prayer. But before you benefit from such a touch of lenity, look to suffer in some heat.

Blanchefleur. Ha!

Benoît. I know what is promised.

Bailleton. Flogging, half-drowning, breaking bones

In quest of further information

Before the final picture of distress.

Blanchefleur. No!

Bailleton. Imagination falters as I think

Of what may yet become of you today. Benoît. More of an ancient's sense of justices?

Bailleton. Yes, every fault to be punished at all costs in any fashion!

Enter Maxime and Louise

Blanchefleur. I hanker for no old man's judgment here.

Bailleton. The duke will render one nevertheless,

Not likely to be liked by anyone

Who once took care of you, as I do here.

Blanchefleur. What have I done?

Bailleton. Killed your baby, called murder in these parts.

Maxime. Exactly as we feared when she took up

The monster in her arms to milk its lip!

Louise. Confirmed! For all our coddling, looseness first,

Then murder.

Blanchefleur. It choked before you came.

Bailleton. I did not see that.

Blanchefleur. Will I die here before we have a chance

To speak a little for our hapless cause?

Maxime. She has lived, to our torment.

Louise. Too comfortably, as I often say.

Blanchefleur. Will not a maiden be believed at least

By those she loves?

Maxime. That much depends on what the duke decides.

Louise. The crime and then punishment, I say.

Blanchefleur. I could tear off these hands for casting that

Dead thing before suspicion could see it.

Benoît. Tear off your hair at least, or mine at worst.

Maxime. The fifth case in our neighborhood this year!

Louise. The Simons only yesterday at dawn!

Bailleton. I weary in attempting to catch all, Youth at all times so often at it still.-

The duke in thunder-clouds of indignation!

Enter the duke of Mayenne, attended

Mayenne. Is this the murderess?

Bailleton. It is, your eminence.

Mayenne. The magistrate some think too lenient in

Child-killings is not here to try this case,

So that it but remains for you to tell

Your story to your duke, for which come forth.

With fearless speaking tell me in few words

Why you at fourteeen have destroyed your child.

Blanchefleur. My lord, I killed no one.

Mayenne. You know the fears the guilty are subject

To for untruths in chambers of Bastille.

Blanchefleur. I do not, nor with trembling do I seek

To know them yet, because I speak the truth.

Mayenne. How would it be if we let murder slip?

Can states stand in such cases? Tottering,

The powerfullest must by nature fall.

You might aver you merely killed a babe,

Moreover, as I hear, the merest lump,

Bereft of voice and almost half his face.

Yet what of that? You stifled living breath,

Created as we are, though probably

Too weak to live out many days. Admit

Your fault, and suffer what is promised in

Such cases.- Do you weep? That demonstrates

Guilt fitly trembling in her honest mask.

Blanchefleur. I cannot speak for fear.

Mayenne. Most obvious proof of guiltiness

As any yet in court! Confess. Spare pains

Too few of any age or sex can bear,

Or else be bound inside to instruments

That, tearing, searing, speak with iron tongues

Instead of yours.

Blanchefleur. I hurt no none, my lord.

Mayenne. Few will misunderstand the reason why:

No father for your babe! Too plain it seems

You rid yourself of worry to ease life,

Unthinkingly, remorsefully. Then say

To all the world: "I killed my babe," so that

One truth at last may breathe, though he does not.

Blanchefleur. I sigh to say: "I never killed my babe."

Mayenne. Untrue.

Blanchefleur. A witness, kindly lord!

Mayenne. That boy? I think he shrinks apart because

He is as guilty as you are, and thus

Will likely suffer the same fate as yours.

Blanchefleur. No, no, no, no.

Maxime. My lord-

Mayenne. Our troubling donkey-mocker once again?

Louise. Your eminence, however that may be,

We now believe the child is innocent.

Mayenne. Who else was witness to this felony?

Bailleton. I was, your emicence.

Mayenne. You saw her kill her babe?

Bailleton. Oh no, my lord.

Mayenne. Who then saw her do it?

Bailleton. None, as I think, my lord.

Mayenne. Though no one saw it, she should be condemned

As any sorceress who practices

At night the vilest stiflings, witness-poor

To our designs of ridding us of them.

Maxime. Is it not worse, my lord, to execute

The innocent than freeing culpables?

Mayenne. No. Innocents towards home sink to rise,

While guilty ones make earth the thing it is,

Most horrid and despicable. I say

She's guilty: can you counter otherwise?

Maxime. No.

Louise. And yet she's innocent, too innnocent.

Blanchefleur. Ho, what of that? Most guilty are we judged

To be, and therefore as the guiltiest wail.

Mayenne. Not so. I now believe the girl and boy

To be quite innocent of any crime.

Blanchefleur. Ha?

Mayenne. No one can tell here, therefore no one dies.

Bailleton. Not choking on a gibbet, it appears.

Benoît. No bleeding on this day: all quit with sweat,

Less painful by far.

Blanchefleur. For all deeds once remembered or else not,

A promise to atone repentantly!

Mayenne. What do you think, Bailleton? Should they at least be whipped to rawness for promiscuity?

Bailleton. Look how the merest word sends liberated youth a-tremble! Your eminence, for many years I have been enjoined as lasher royal on multitudinous shoulders of infraction, with few thanks, but, to this day, I have rarely seen a case demanding that I bestir myself as this one. I promise to bleed lasciviousnesses to their knees in tears, by this hand.

Blanchefleur. Too cruel officer, my thighs have never yet even felt rough homespun.

Mayenne. For once, your pained body will be stretched and twisted against the pole of blood as tightly as the skein you work on. How will it be, beadle: leather, wood, or steel?

Bailleton. The expert blisters both with one pole-chain.

Blanchefleur. You cannot know me.

Bailleton. Fainting at this time? The girl I do not know, neither her limit nor mine. As for this fellow, I know him.

Benoît. But I do not, only my backside does.

Mayenne. Prepare, while fathers mutely stare and moan.

Exeunt Mayenne and attendants

Maxime. Before all great ones, bend submissively.

Louise. How else should carelessness be made to learn?

Blanchefleur. You will not strike indecently, kind sir?

Louise. Expect to bleed where once you should have bled.

Blanchefleur. Some kind of pity, gentlest officer!

Bailleton. The law appears to be insulted here,

But I learn patience with my Seneca:

A promise of an execution on

Your arses if not on your guilty necks.

Benoît. To be macerated into long strips of flesh for disposing of garbage!

Bailleton. Enough of seeming tears, more of real ones!

Blanchefleur. A man certain to leave deep impressions on us.

Benoît. His rods if not his name.

Bailleton. Both quite likely, in that "Bailleton" is inscribed on each of them.

Exeunt Bailleton, Blanchefleur, Benoît, Maxime, and Louise

Act 4. Scene 4. The church of St-Andrew-of-the-Arts in Paris. 1593

Enter Father Aubry and Barrière

Barrière. The outcome at Suresne will please no saint.

Aubry. A three-month truce against the Protestants

Is Satan's coronation triumphing.

Barrière. Which we prevent, before the Huguenots

Rest without needing to hide from God's wrath.

Aubry. In your hands ready to be tried and done

With glory on your crown. Will you do it?

Barrière. What, killing a non-king, and for a cause

Revered by those we hold as godly? Yes.

Aubry. King David's benedictions on such oaths!

In holy water will we wipe those hands

With powder dirtied for the Béarnais,

That Holofernes and a hypocrite!

Conversion cannot rise from foggy lamps

Of Calvin's institutions starved in sin.

Barrière. No.

Aubry. Shoot him quite through the guts, though in our church

I bellow it, as yet too secretly.

Barrière. In his back, neck, or elsewhere, so long as

A monarch dies. I am amazed too few

Among the faith have yet attempted it.

Aubry. The French are God's cold dishes, which is why,

To show us how, after that action's weal, With Judith you will banquet luciously.

Barrière. No doubt.

Aubry. Go, Peter: I will build on you alone.

Barrière. The Catholic anew in God's own France

Despite our hearts of negligence and fear!

Aubry. A kiss for your endeavors! Surpass all.

Barrière. I thank you, father. Though said to be brief

With most, I'll be far briefer with this king,

Much to his dolor as he groaning lies,

To sludge where all the heretics slime off.

Aubry. As many benedictions on this aim

As I speak words wherever congregate

The faithful when they kneel to saints at work!

Exeunt Barrière and Aubry

Act 4. Scene 5. A street in Paris. 1593

Enter Maxime and Bévue

Maxime. A suitor for my niece while you stroke down

My hair, with everything that climbs with love?

Bévue. Yours to be dallied with too secretly

But meet, hers in the daytime openly.

Maxime. A matter of deep lightness never seen

In stories of Boccaccio I have read!

Bévue. I trifle with your niece's openings,

While yours complete my own, to fill up well

Desire's leaky tub to overflowing.

Maxime. How will it be when my wife contemplates

Our mutual fingering, as must at last

Be found, however we disguise and feign?

Bévue. To prove it is not so, I'll cover both,

To their most sweet content, with yours as well,

Disguising our intentions as we sway

In secret from the keenest probing eye.

Where does she lie?

(Groans are heard within

Maxime. Your answer: Blanchefleur moaning on wet sheets,

Regretting much the zeal of officers

Of law against non-crime unjustly found

And punished cruelly.

Bévue. Still smarting?

Maxime. Just barely feeding without scarcely

A motion of her body pent in gauze.

Bévue. That beadle I hope to be quit against,

If once I own the duke of Mayenne's ear.

Maxime. Go comfort her in any way you can.

Bévue. Miraculously rising friend, I will.

Exit Maxime, Blanchefleur revealed in bed

How do you fare, of all my sweetest sin?

Blanchefleur. I think, when naked, I shine in the dark.

Bévue. I'll be avenged against that officer.

Blanchefleur. Do. Let me hear but once before I sit,

Should that be possible next month or year,

That nervy-membered Bailleton has been stabbed

Across his chest in many painful spots.

Bévue. A man for senseless flayings only fit.

Blanchefleur. Indeed, that officer was very wroth

And backward in my case, though innocent

Of any damage done to anyone.

Bévue. Ho! Can you stand?

Blanchefleur. Not without wincing for an hour or more.

Bévue. Ah, dearest! And your friend?

Blanchefleur. I never thought to hear a boy screech so.

He seems one broadside breach, infested in

A way to sadden his physicians as

They hourly tend to shoulder, hip, or sides,

His cannon lost in waves of rising flesh.

Bévue. Your stern-flags lowered as his own, I guess.

Blanchefleur. I am the creature with one buttock, since

The crack is lost on which a maiden rests.

A stick of fire! The hissing and the cut!

None should imagine bodies fissured so.

He dove into us, opening portholes

As if he meant to drop with sweat and blood

Into a wider Seine. When first that bar,

That awful, awful, awful rod of pine,

Which often he replaced as it wore out,

Bore on four shoulders as we kissed the post,

I tumbled without falling in a kind

Of fainting watchfulness, thighs like the top

Of trees in rougher gales, breasts flattening

Against my pillar, lovelessly erect.

Bévue. For this, a man will loudly shed more tears

On his own rods than what imbibed that shirt.

Blanchefleur. It mattered little whether back or arse

Was covered: down it came, when every stroke

Burned into flesh wherever it incised,

So that two voices died off after yells

In rounds of misery undreamed of yet

In health or sickness. Look with wondering

At linen cut away, which once was thought

To be my petticoat: so many blows,

So many yelps of dolor, till the man,

Or rather human brute unknown of men,

Lost breath in digging wounds inside each wound.

Bévue. Say how may I best serve you in this gear?

Blanchefleur. Despite her pains, the punished should still eat.

Bévue. Come. I'll support your strides along the way.

Exeunt Bévue and Blanchefleur, tottering and groaning


text:
Collaborative play writing/French chronicles of the 1590s/Act 5

Act 5. Scene 1. A street in Paris. 1593

Enter Bailleton and Barrière, bound

Bailleton. We will discover how our laws resolve

In full a king's would-be assassin's case.

Barrière. Ah, had I done it! The world would have changed as I wish it. Now I'm a kind of nothing, soon to be even less.

Bailleton. Not before I handle you, for the sake of a country's example.

Barrière. A mere word meant to scare, as when a crow

Swoops down behind another to chase it

Away from worms.

Bailleton. You will become the box to feed those worms.

Barrière. All my hope now, before the life to come.

Bailleton. Expect no peaceful exit from our scene.

Barrière. I do not. A peaceful plague on you with every Catholic puppet of aspiring Protestants!

Bailleton. I'll very much pity you when the fury of my beam takes precedence over pity.

Barrière. The duke of Mayenne's man to sentence me.

Enter Bévue

Bailleton. You have in hand the duke of Mayenne's seal?

Bévue. I do. Here it is.

Bailleton. Verily his own. Pronounce the duke's wishes against the convicted assassin, though not one.

Bévue. By order of the duke of Mayenne, hear your sentence: your right hand will be burnt, your legs and arms broken, your body left to dry on the wheel for as long as the duke of Mayenne feels inclined, then, in the evening, you will be strangled to death.

Barrière. Ha, ha, too much perhaps for man to bear!

Bailleton. What, kissing stones and dirt? Barrière, your name

Alone presents a bar to charity.

What heralds promulgate I execute.

Bévue. What of Martout, our executionner?

Bailleton. By the faith I owe to my office, sneezing and spitting in his bed, having stood too long in the rain while working on Bastien at the wheel.

Barrière. Some pity at this time!

Bailleton. A heartless exclamation! Do I stare

Or not on a hoped-for assassin's face?

Barrière. Spare a little. Plead for me, I beg.

Bailleton. No one remains to plead for you. When you

Take arms against a king, you are alone.

Barrière. Sir, sir, sir-

Bévue. There is no weakness in such cases, fool.

Bailleton. Of course not.

Bévue. One who will feel his folly thumpingly.

Bailleton. A matter without saying, as I say.

Barrière. My only hope is for neglect to blink

At feeling arms and legs after one blow,

Or, better still, one who will fail to count

Above a score of one.

Bévue. Facilitate your arithmetics, beadle, by taking into account, as Fibonacci did, both the nature of the numbers and their position.

Exit Bévue

Barrière. Huh, mercy, mercy!

Bailleton. Let us together see what shackles, fire,

And a long iron bar accomplishes

On that most criminally detested form,

Deserving pittance in the way of ruth,

All our tools senseless to the sighs and groans

Of culprits held in pain, as pinioned as

They were to lawlessness and liberty. Barrière. Where is my priest? Not here with me, I see.

Bailleton. Few would choose to be with you at this time,

But if you speak of Father Aubry, I

Suspect he will not be left off so soon.

Barrière. You know of him already? Is he dead?

Bailleton. As if dead when interrogated by

Some of my fellows, loath to dandle friends

Of murderers.

Barrière. Help me escape. I'll give you bars of gold

From churchmen promulgating my attempt

As blessedness in action.

Bailleton. No dodging from the dodgeless possible,

Unless the public wheel, by gentlemen

With hats watched over carelessly,

The roughest roadway to our lowest end,

Can be considered one, to take you off

To hell's mouth, boneless, or to nothingness.

Barrière. Argh, argh, argh!

Exeunt Bailleton and Barrière

Act 5. Scene 2. A court of justice in Paris. 1594

Enter the dukes of Mayenne and of Feria

Feria. I'm hurried off precipitously by

The self-styled king with much finality

Without formality.

Mayenne. The king is crowned now, first as king, then, what

Is even higher, as a Catholic.

Feria. Is Spain so little taken notice of?

Mayenne. My good lord, do not take it so, but go.

Feria. Will neighbor France turn Protestant before

Our darkened faces?

Mayenne. Cut off my gullet with the sharpest edge

Of bedside crucifixes should France hymn

Her reverence with Luther's dogs and wolves.

Feria. The pope demonstrates by silences

Benevolent and sane, unhurried in

Majestic ire, he in no wise believes

With you in false Navarre's conversion-

Not a conversion from the Béarnais,

But a diversion, to your hopeless loss.

Mayenne. I hope no one believes Mayenne will sink

Beneath the cloudlets of an atheist's frown,

So long as lightning gleams against his side.

Feria. Then why in this foul weather is it not

Out thundering on crownets of such slaves?

Mayenne. A flash of nothing at this something king.

Feria. Some lords have not abandoned. Why then you,

With boy Aumale, behave as traitors here?

Mayenne. Let it be so.

Feria. The duke of Nevers waits for both of you,

And his reward for this is waiting still.

Mayenne. Then let Gonzaga wait.

Feria. First Saxony, drunk with the fatsome beer

Of ninety-five carouses, then the prick,

Too narrow for the codpiece of a king,

Which must enlarge two wives, not one, now France-

Mayenne. Beware.

Feria. Should bigger Spain beware?

Mayenne. Tread speedily with step austere to Rome

Or Spain, while France cares for her own within.

Exit Feria, enter the dukes of Guise and of Aumale

Aumale. Too puny to contend with this green king,

We bicker mightily among ourselves.

Guise. Always to be of use to royalty,

We jostle now for places, not religion,

Aumale. I but require my havings back again.

Guise. What losses have you suffered, lord Aumale?

Aumale. No luck for me as yet in this regime

When Amiens varlets, bolder with the rise

Of royal puissance, resolutely push

Me off my dukedom.

Guise. Not so!

Aumale. So much so that I aim to pash them all

If I can levy forces on their head.

Guise. Yet I am angrier with my dukedom kept.

Aumale. Why?

Guise. A foolish captain of the garrisons,

Saint-Paul by name, initiated plans

To change my own, and so with my two hands

I sabered him.

Aumale. More tragedies unlooked for! I knew him,

But yet I ask your pardon, waspish lord,

For so distractedly has my head whirled

In meditating on accessions

That I can little think on miseries

And deaths of others. My lord of Mayenne,

What are your thoughts on mine and his mishaps?

Mayenne. Loved lord, all these like dust above our graves.

Aumale. No mightier whirlwind of expostulation?

Mayenne. To stay wise I think little and say less.

Aumale. My lord of Guise, your exploits ring aloft

As awful knells on armies who oppose.

Guise. For Henry's sake, I forced into submission

Reims, Saint-Dizier, Guise, Joinville, more, I hope,

Wherever I advance the brave to fight.

Aumale. What other business should we meddle with?

Guise. The case of Father Aubry, as I hear.

Aumale. True. Shrewdly no doubt rightly held

For his attempted murder of the king.

Guise. Should we not rather say arraigned at worst

In an attempt at virtue evilly

Misplaced in changing times?

Aumale. The priest, by Aaron's calf, will soon be seen

By those who honor truth like honest wives

As homicide's resource, ungilded from

The lilly of his surplice, or the gloss

Of his gold chasuble, however meant

To soothe or teach parishioners in doubt.

Mayenne. We'll narrowly and sharply question him.

Aumale. Where are the bars and pincers?

Mayenne. No need of those as yet.

Guise. My lord Aumale, if you remain so still,

We speak about a priest in these debates.

Aumale. One who fomented plots of a king's death,

One who, despite night-guardsmen, may succeed.

Guise. The priest is guiltless. Otherwise, we are

As guilty as he is, in having planned

A king's demise as often as we charged

His hosts in battle.

Aumale. Nevertheless, we'll deeply search inside That heart, perhaps extracting from one leaf

Some holy poisons men disgorge to find.

Guise. Opinion is not guilt.

Aumale. In my view, Father Aubry should be tried

And then convicted, to be led away

With only his head as possession.

Guise. We'll see perhaps.

Mayenne. Bailleton, bring in the prisoner at once.

Enter Bailleton and Father Aubry, bound

Mayenne. Stand for confession, priest of murder, or

Expect your seat to be in irons fixed.

Aumale. No boldest mouth of contradiction here

But plainest truth, with none of that incense

Betrayers puff out to equivocate.

Guise. Astonished father, do not stare afraid,

But, as my lord Aumale in smoke suggests,

Speak truthfully if you desire to live.

Aubry. I do, my lords.

Mayenne. Did you plan the king's slaughter with Barrière?

Aumale. My lord of Mayenne, no.

Guise. You knew Barrière?

Aubry. Yes, as a faithful and true Catholic.

Aumale. Yes, as a faithful and true murderer.

Aubry. No, as a faithful and true Catholic.

Guise. You knew about our truce with heretics?

Aubry. A heretic one.

Mayenne. A necessary one. My reverence

For sacerdotal vestments hinder me

From striking off your collar with your head.

Aumale. You knew Barrière, a truth Séguier revealed

To us, who saw you lovingly embrace

Next to the altar treason's instrument,

As ugly a kiss as was ever found

On French ground, or wherever loyalty

To princes of the world in peace appears.

Aubry. Séguier, unkissing Judas, execrates

That kneeling figure in the olive grove

Which ever blossoms rooted to my soul.

Aumale. In you I see their sword, never his peace.

Say: did you also know as certainly

That villain's aim to cut away our king?

Aubry. I did, your eminence.

Aumale. Enough. Condemn the traitor to the wheel.

Guise. Lord of Aumale, more patience if you can

But summon that, although unquietly.

Aumale. This winter-priest, whose branches show dead leaves

Of Gospel truth, suborned the murderer.

Mayenne. He's Judas-guilty of political And irrelegious murder, by my love

Of roughest virtues in a kinder realm.

Aubry. My lords, I never paid him for this piece

Of work, though seemingly so wonderful

When first he spoke of his intentions.

Aumale. Who has an ear when man foredooms himself?

Guise. He knew of it without inciting him.

Aumale. Still guilty, still a traitor. Split the knave.

Aubry. True, guilty in my love of God's religion.

Mayenne. He's banished.

Aumale. Out, civic disobedience, to a death,

Much crueller than most, outside of France.

Guise. A sentence rather just. Away with him!

Bailleton. My lords, uncover condemnation's goal:

Should I beat on his head as he slogs off?

Guise. What, bloodiest hands on a conforming priest?

Aumale. Lead him away more gently than his kind

At our hands merit, piecemeal mashing him

Should he attempt escaping from our gyves. Mayenne. Priest- should one falter to misname you so-

Let none in France observe birettas, stoles,

Or cinctures of your own, unless you wish

To mourn in painfullest ways known some loss Of members To Bailleton, mercy's truant of our laws.

Exeunt Bailleton and Aubry

Aumale. Much work for us in France, my lord of Guise.

Guise. May Henry, fourth king of that name, live long

To recompense more plenteously such work.

Mayenne. First deadliest foes, now truest subjects known!

Aumale. In no way must we be surprised, my lord.

In knowing life from life, we recognize

More to existence than mere thoughts of men.

Exeunt Mayenne, Guise, and Aumale

Act 5. Scene 3. In front of Maxime's shop in Paris. 1594

Enter Maxime and Bévue

Maxime. She lisped at him while you stood blinking by?

Bévue. Your wife accosted Bailleton, torment's son,

Inviting him as Venus' favorite

To enter into woman's choice retreat.

Maxime. Hah? Where?

Bévue. Inside your house.

Maxime. When?

Bévue. Now, after eating all their bellyful

Of spicy meat.

Maxime. That officer is at this moment in

My house pinned lovingly to my Louise?

Bévue. He is, though still you must not yet go in.

Maxime. Must not, Bévue? Impede me if you can.

Bévue. Hold off.

Maxime. Am I as in a confirmation crossed

On my cornudo's forehead near the fane

Of love while we discuss the time away?

Bévue. Most certain, dearest mongoose. By this time,

They will have been undressing, scattering

Their clothes disorderly, to lip and play

While standing in a sweaty ague, yet

In need of no physician's herb or pill,

Unless it be their tongues, at work on mouth

Or groin, which first augments the malady

Few would prevent, and then at last allays.

Maxime. Good.

Bévue. You fail to fathom friendship's fondest fool.

As when we fixate on a point in space

While riding, farther persons shift our way

When nearer ones move oppositely, so

A friend proceeds as wished for when the wife

Becomes contrary. Yet you gain by this.

The mongoose catches twined snakes in their hole.

While they cavort, we'll frolic pleasantly

As lovers rarely do with the spouse

So dangerously near their hairy knots.

Maxime. I love and hate that scheme.

Bévue. Although injurious to your heavier brows,

A pastime to be savored breast to breast,

Or thigh with thigh transfixed in Andrew's cross.

Maxime. A vision all too keenly biting me

In kitten play astride temptation's cage,

A prelude to our homorhythmic stance.

Bévue. Through my door enter, not your own as yet,

Inserting swiftly keys to pleasure's house.

Maxime. Spruce mischief, thereabouts I can. What then?

Bévue. You keep a club, like Hercules' not

Intended only to affright starved cats?

Maxime. I do.

Bévue. One that can dent the massacrer of

Your honor, Vulcan-netted on your sheets?

Maxime. With laughter mammocking both head and breast.

(Groans are heard within

Bévue. But hold. What horrible complaint is this?

Maxime. Is it Louise's?

Enter Louise, crawling

Louise. O! I am maimed forever. O! O! O!

Maxime. This nearly buries sight in darkest pall.

Louise. O! O!

Bévue. It seems Bailleton is not to be seduced.

Louise. He was, almost to amorcide, as I

With winking nods, coy looks, and quivering,

An adder coiling on her colder mate,

Removed my shirt, according to our plan.

Bévue. He did not grunt while entering the coach

To ride atop soft Venus' tufted hill?

Louise. No. I looked to take out his breeches' staff,

But found instead a larger one, which he

Employed not to the soreness of my sides

But to the utmost peril of my bones.

Maxime. That leg is badly broken, I suspect.

Louise. Oh, help! Not touchable without worse pangs.

Pain as I never knew, and worse to come!

Maxime. Not movable without much worse than worst.

Bévue. Where is the coney-sensing officer?

Louise. Quite likely with his master to consult.

Maxime. Will I be flicked on once again because

You tried to stamp me on a foreign coin?

Louise. The duke of Virtue may imprison us,

Suspecting your approval of our plot.

Bévue. Much to be feared, alas, for all of us!

Maxime. As cuckold almost published, to be charged

Besides as your unwitting wittol! Ha!

Enter Bailleton

Bévue. Sir-

Maxime. Sir-

Bailleton. Foul nestling of adultery and her

Abettors whistling in their deepest fear!

Maxime. Sir-

Bévue. Sir-

Bailleton. This cannot please a duke by day or night.

Maxime. Ha? Of so small a matter, easily

Explained, have you already notified

The duke of Mayenne?

Bailleton. I have.

Maxime. I fear our jestings are misunderstood.

Bailleton. I understand this woman is your whore.

Louise. See how our weasel trap recoils on me.

Bailleton. Moreover, as experience teaches one,

I understand a harlot's punishment:

A frisky lashing on the shoulders, bared

For sweaty leather, barer as I ply

At them with rigor's office till she mends.

Louise. How will I stand to flesh-dissolving blows

With one leg broken as you plainly see?

Bailleton. I'll whistle downward as you lie aground.

Maxime. You will expose your end, wife, as the end

Inevitable of habitual

And careless whorings, almost to my face.

Bailleton. Philosophical whoremaster, do not

Think to escape with female penances.

Maxime. What have I done?

Bailleton. Suborned this creature as your source of pay.

Maxime. No, no, no, no.

Bévue. What strange persuasions do you entertain

Concerning my best friend? Maxime as pimp

Of his own wife, beloved as few have seen

In garden paths while strolling arm in arm?

Bailleton. I think he is. I also think you help

That wife-procurer as his friendly bawd.

Maxime. No, no.

Bévue. No, no.

Enter the duke of Mayenne, attended

Maxime. My lord-

Bévue. My only honored lord-

Mayenne. Hold off. Each will be questioned patiently,

So that the truth in every word you speak

Becomes more generally known to all.

Bailleton, speak boldly of discoveries

On newest meshes of laciviousness,

Exposed to catch unwary flies of sin.

Bailleton. This woman, chained to lust as sailors to their mast when storms blow, if you will frowning hear, attempted me before her house as I was striding by contentedly.

Mayenne. How was she dressed? What question did she ask?

Bailleton. A whore's dress, as innocents may notice, holes at the front for easier entry, with a whore's queries concerning wants and money.

Louise. My lord, these are some poorer woman's clothes

Than what your officer is used to see.

Mayenne. Back to your tale, beadle.

Bailleton. Or rather backward to her tail. She turned and showed me that, with many sighs and groans pointing the way towards her house, which I shrewdly suspected as the woman's pit of infamy, where, slipping off skimpy veils, not clothes, in an alcove whoozy with Provence perfumes, she eyed me askance, pointing all the more salaciously to her body and the bed, as I pretended interest for the sake of public morals.

Mayenne. Do you deny this, trollop?

Louise. My lord, no. Yet hear.

Mayenne. Hear your accuser first, and then prepare

To bleed somewhat.

Bailleton. To my disconselate view, she negligently took off her shirt, as trifling as a hat, in open-mouthed passion straining and puffing, with many invitations to lie alongside fur and Levant coverings, as if the dark between white bulging thighs should swallow mine and a dozen more.

Mayenne. That shirt must be taken off again before you quit yours, with the result that she'll squirm as expected, but not with same joyance as she hoped. What of these two?

Bailleton. Confederates, I think.

Mayenne. The joyful ass! How, pander to his wife?

Maxime. I deny that, my lord.

Mayenne. This is your house, no? This is your wife, no? I think by associations you are likely to be very guilty, together with my herald, as a friend intending to entice for money. Enough. To scrutinize further into such depravities would be too fulsome for any honest eye.

Bévue. Your eminence, as herald and representer, know that I worship my occupation as never yet, love the emblazoned fields of honor on your shield, enjoy beyond redemption your glory and my honesties, respect the style of rank and emblem in dextrals or otherwise, the badge of arms in truculence or peace. May I not keep them and remain truly and reverentially yours, hopefully forever, as my very worshipful duke of Mayenne?

Bailleton. What is your pleasure, justest eminence?

Mayenne. Rip off his livery to barest parts Of nakedness.

Bailleton. The gladder for the pride he feathers on.

Maxime. Ha!

Bévue. Deserved! With clothes he should flake off the flesh.

Mayenne. Where is your cudgel, worthy officer?

Louise. The bastinado and, I fear, much worse!

Maxime. We'll squeal as he adds weals on top of weals.

Bailleton. Here for their service, though unwillingly.

Mayenne. Remove their shirts, as prelude to the loss

Or damage to some portions of their skin.

Bailleton. Done, best of lords.

Mayenne. Beat them to weariness at farthest ends

Of Paris suburbs cleanly, thoroughly,

As if you meant to sell three Persian rugs.

Bailleton. For justice's sake, I will, my honored lord.

Mayenne. Give them ten thousand reasons to weep hard.

Exeunt Maxime Bévue, bearing Louise, with Bailleton, enter the duke of Aumale

Aumale. My lord, you are awaited by the king.

Mayenne. The faster to bind up fresh-bleeding France.

Exeunt Mayenne, Aumale, and attendants

Act 5. Scene 4. The cathedral of Chartres. 1594

Enter the archbishops of Lyon and of Bourges

Lyon. Although I shame to admit hesitations, doubts, fears, suspicions few yet blame me for, you appear to have been in the right, archbishop of Bourges. The king is reinstructed in rudiments of religion, as if newly baptized, crowned both as a Catholic and king, for which hymns should cathedral-wide reverberate throughout cathedrals in France and Spain.

Bourges. No doubt through doctrines eruditely attained in arduousness of study in a fashion congenial to the king's grounds of fundamentals in our matter, with other priests happily and irrepressibly minded to teach him the principles we cherish, Father Lincestre must be thanked by citizenries that no soldier's sword or musket stir and fire in our streets, as has been our sorrow's outcome since the duke of Guise's cheek was scratched at Vassy.

Lyon. Because of which the prince of Condé upreared Goliath-like as his enemy and religion's, until his capture at Dreux.

Bourges. Which might have finished religion's martyrdom, when the same Francis, duke of Guise, was surreptitiously shot to death by Poltrot de Méré.

Lyon. A Huguenot putrid in our memories!

May the entire faction lie where is,

And rest there dead.

Bourges. In any case, may Henry the Fourth go as our king, his armies clattering towards Paris and perhaps- may that perhaps live!- our peace.

Enter Father Lincestre

Lincestre. What signs of trouble a good man yet beholds!

Bourges. You refer to Father Aubry's condemnation?

Lincestre. In his path to exile monstrously transformed, no more the spry and wicked defender of religion, but a sadder one, alone and stumbling away towards outsideness. Lyon. Deserved.

Bourges. Deserved, with wraths of penance on his head!

Lyon. Bad priest.

Bourges. Worse man.

Lyon. A reprobate too much tolerated by us.

Bourges. Avoided now, which with timbrels and songs should be encouraged and blared forth wherever he goes.

Lyon. His jailer should have pressed Barrère's ashes on his eyes. à Lincestre. And yet there's charity.

Lyon. Provided he amends, for otherwise

An added punishment, or death to him,

More quickly!

Exeunt Lyon, Bourges, and Lincestre

Act 5. Scene 5. A street in Paris. 1594

Enter Maxime and Bévue, bearing Louise, with Bailleton beating them

Maxime. Ha! Ha! My shoulder!

Louise. O! O! The inside of the thigh, and worse!

Maxime. Some of your gentlest mercies, sir!

You see she cannot move her leg, so that

We torture her by plodding gingerly.

Bailleton. However that may be, the duke pronounced

Your sentences, which I will consummate.

Maxime. Ha!

Louise. Ha!

Maxime. Unpitying officer! Take note, we pray,

Of unknown murderers along the way

Who very likely shed some tears for us. Louise. How long still?

Bailleton. We go where I have never gone, to the farthest limit of this street and beyond that to another, extending to another until another.

Maxime. When will you begin to pity us?

Louise. What should we do to stop the progress of pain's procession?

Bailleton. To continue crying out with promiscuous teardrops is your hope, best serving as examples to Parish citizens along our slippery way, covered with remains of flesh and blood, who for this time fearfully contemplate the consequence of vice.

Maxime. Ha! My neck!

Louise. Ha! The leg, that leg again!

Maxime. More pains, more pains, and more.

Louise. How will this continue?

Bailleton. How otherwise than with further trouncing? A promise was made to beat you whether you fall or not, to beat you as you continue shouting in pain or not, beat you by day or night, beat you in the city or in the suburbs, beat you in thoughts to amend you, beat you as an afterthought, beat you all in all for all in all.

Enter Blanchefleur, limping

Blanchefleur. All these footprints of blood on every stone

Infallibly leading towards you!

Maxime. See, girl, how sometimes partly, sometimes completely we are martyred.

Bévue. All this deserved.

Maxime. Officer, you strike too hard on my friend's head, so that he seems to rave in a way I cannot like.

Bévue. I say, merited, and will add proof on proof, once I stand beside my bed and studiously consider our plight.

Louise. No quarrel, till my leg is tended to.

Bévue. Not Avicenna's canon will help us

Cure all our injuries, deserved, I say.

Blanchefleur. Knock on your heart, officer, to verify whether it is harder than your cudgel. How lamentably will you regret two-armed vigor when one day requesting pity for yourself! For who does not?

Maxime. That's so, according to her philosophy and mine.

Louise. What do you say on this?

Bailleton. I, say?

Maxime. O!

Louise. Ha!

Bévue. Ha!

Blanchefleur. Why do you hit them harder?

Bailleton. I, say? I say nothing. Here's for you and further sayings.

Maxime. Ha! Can such things be?

Louise. Husband, I pray you, do not wobble so much when he buffets you, since it grieves my leg all the worse in untold miseries.

Bévue. O!

Bailleton. Be thankful that your punishments are no better, so long as you continue yelling out in pain, excellent emblem to edify a people, some of whom stare and hesitate, watching and praying that none of them will one day be commanded to strip and bend even once below signs of my mastership.

Blanchefleur. Remote clouds pity, but not formality in his marble pose, uneroded by rain. Robins peck, amaranths bloom, bloody men dig graves.

Maxime. Piteously we go forward without advancing.

Louise. More on top of more.

Bévue. More because of mores.

Maxime. His mercy sleeps behind an iron door,

Too rusty to be opened for our use. Blanchefleur. I cannot walk with or without you.

Louise. More.

Maxime. And more. O!

Bévue. Ha! Head and leg together with one blow?

How is it possible? I dream or die.

Blanchefleur. To the end of the way with pity's mouth awry.

Exeunt Maxime, Bévue, Louise, Bailleton, and Blanchefleur

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
User:ZooLondon

I am a new young writer in the UK wanting more experience and to build my writing portfolio. I have recently begun doing some technical writing for my employer, which mostly revolves around a specific IT system and standard operating procedures for the company's quality management system. I'd like to make a name for myself and perhaps get some freelance work in future, and this looks like a good place to start!

title: User:ZooLondon


text:
User:Alan Babcock

I am an Educational Psychologist. I belive I can contribute in both fields.

title: User:Alan Babcock


text: User:MyDogShotJR

title: User:MyDogShotJR


text:
File:R1.3.14.png

Licensing
for school project

title: File:R1.3.14.png


text:
MediaWiki:Recreate-moveddeleted-warn

Note: You may develop a new Wikiversity resource under the same name as the previous deleted resource or request undeletion.

title: MediaWiki:Recreate-moveddeleted-warn


text:
Dominant group/Genus differentia definition

"A genus-differentia definition is a type of intentional definition ... composed by two parts:
 * 1) a genus (or family): An existing definition that serves as a portion of the new definition; ... [and]
 * 2) the differentia: The portion of the new definition that is not provided by the genera." Bold added.

There are rules for definition by genus and differentia.

“Where a synonymous definition is unavailable or inappropriate, we can use a definition by genus and difference.” “The possibility of defining terms by genus and difference depends upon the fact that some properties are complex, in the sense of being analyzable into two or more other properties.”

“One defines a term by genus and difference by naming a genus of which the species designated by the definiendum is a subclass, and then naming the difference which distinguishes it from other species of that genus.”

Dominant group may lend itself to this form of definition. Alternately, its relative synonyms may fit into a pattern of genera differentia.

Theory of definitions
Def. "[a] distinguishing feature which marks something off from other members of the same family" is called a differentia.

Def. "[t]he attribute that distinguishes a species from others of the same genus" is called a differentia.

Def. "a rank in the classification of organisms, below family and above species; a taxon at that rank" is called a genus.

Def. "[a] group with common attributes" is called a genus.

Def. "[w]ithin a definition, a broader category of the defined concept" is called a genus.

Rules
"Certain rules have traditionally been given for this particular type of definition. " which are
 * 1) "A definition must set out the essential attributes of the thing defined."
 * 2) "Definitions should avoid circularity. A definition of a term must not be comprised of terms which are synonymous with it.  This would be a circular definition, a circulus in definiendo."
 * 3) "The definition must not be too wide or too narrow.  It must be applicable to everything to which the defined term applies (i.e. not [leave] anything out), and to nothing else (i.e. ... include [more objects or entities] to which the defined term [applies]."
 * 4) "The definition must not be obscure. The purpose of a definition is to explain the meaning of a term which may be obscure or difficult, by the use of terms that are commonly understood and whose meaning is clear."
 * 5) "A definition should not be negative where it can be positive."

Genera differentia
The genera differentia for possible definitions of dominant group fall into the following set of orderable pairs:

'Orderable' means that any synonym from within the first category can be ordered with any synonym from the second category to form an alternate term for dominant group; for example, "superior class", "influential sect", "master assembly", "most important group", and "dominant painting". "Dominant" falls into category 171. "Group" is in category 61. Further, any word which has its most or much more common usage within these categories may also form an alternate term, such as "ruling group", where "ruling" has its most common usage in category 739, or "dominant party", where "party" is in category 74. "Taxon" or "taxa" are like "species" in category 61. "Society" is in category 786 so there is a "dominant society".

Mosby's dominant group
In Mosby's Medical Dictionary definition that a dominant group is "a social group that controls the value system and rewards in a particular society." is a synonym for "ruling": "controls", which is a verb form of "controlling".

Combining two genera ('class' and 'sect') with two differentia ('superior' and 'ruling') provides a series of definitions for dominant group.

Def. a class that rules superiority and the sect is called a dominant group.

This is close to "a social group that controls the value system and rewards in a particular society."

By reducing Mosby's definition to "a class (group) that rules (controls) superiority (value system) and the sect (rewards, such as membership in the sect)", the core meaning of dominant group is isolated. Adding "social" and "a particular society" may not be needed to convey dominant-group meaning but places the definition in several fields such as anthropology, psychology, or sociology.

Alternately, "a class (group) that rules (controls) superiority (value system and rewards) and the sect (such as membership in the sect)" also matches the core meaning of dominant group.

Mosby's five conditions
With Mosby's definition, the essential attributes are set out. (Rule 1)

The genera (class and sect) are relative synonyms of 'group'. But, they can be put into a hierarchy (class > sect). The differentia (rules and superiority) or (superior and rules) are free for multiple uses: 'a ruling class', 'rules superiority', or 'transcends its sect' so as to avoid circularity. (Rule 2)

The genera and differentia must be applicable to everything to which the defined term applies and nothing else. (Rule 3) This requires a careful examination of each of the small group study examples.

The purpose of a definition is to explain the meaning of a term which may be obscure or difficult, by the use of terms that are commonly understood and whose meaning is clear. (Rule 4) Initially, this appears to be the case, but words leading to a precising definition or theoretical definition may be needed as with Mosby's definition.

The genera differentia definitions are not negative. (Rule 5)

Choosing better relative synonyms may resolve any issues with Rule 3 and Rule 4.

Kirby's dominant group
Def. groups of insects whose geographical distribution "extends to the tropics, [but] fall short of the polar circles" are called dominant groups.

For two genera ('class' and 'sect') with two differentia ('superior' and 'ruling') there is the following definition.

Def. a class (group) that rules (extends geographical distribution) superiority (tropics to short of the polar circles) and the sect (insects) is called a dominant group.

Here, the core genera differentia meaning of dominant group is isolated.

Kirby's five conditions
Rule 1: the essential attributes are set out.

Rule 2: 'groups' is an exact synonym for 'group'. There can be a group of groups. 'Extends' is not a relative or exact synonym for 'rules'. 'Tropics to short of the polar circles' is not an exact or relative synonym for 'superiority' but is a value system assigned by Kirby. 'Insect' and 'sect' both mean 'separated' or 'segmented'; i.e., a group of 'separateds' or 'segmenteds'. 'Insect' is not an exact synonym for 'sect' nor is it likely to be considered a relative synonym.

Rule 3: using 'tropics' (Tropic of Capricorn to the Tropic of Cancer) and 'fall short of the polar circles' (Arctic Circle and Antarctic Circle) is an exact geographical extent. Arguments may even be offered using statistics: one ant puts three legs on the polar side of the Arctic Circle while the other three are on the other side may not be statistically significant to say that species of ant has a greater range than a dominant insect group, especially when all the other ants of the species are on the tropics side.

Rule 4: geographical limits such as those used have been commonly understood.

Rule 5: the definition can be written negative but is not.

Kirby's definition of dominant groups of insects is rigorous or can be made such with an application of statistics.

Economics dominant group
In the economics article cited following: "sect" is used as "section", sections of the article itself, "class" usually refers to a "class of test statistics", "superior" refers to a "superior predictive ability", and "rules" refers to "decision rules" or "trading rules". A definition of dominant group per preceding cited article (only using three of the four genera differentia) may be

Def. a superior class [of test statistics] that [influences] [decision or trading rules] is called a dominant group.

Other definitions are likely. In the above article, the word "dominant" and the term dominant group did not occur.

A second article suggests some other situations. In the citation following, "class" refers to "A majority group, say, the workers, who control the policy might rationally choose to have a constitution which limits their power, say, to expropriate the wealth of the capitalist class.", "the class of feedback policy rules", and "[t]he most general class of decision policies"; "sect" refers to article sections again; "rules" refers to "policy rules" or "decision rules"; and "superior" refers to "Typically the iterative process of the policy rule change inducing investment function change inducing policy rule change, etc., did converge. Given that it converges, the limiting policy rule is consistent in the sense described in Sections I1 and IV. In all cases for which it did converge, we searched for and found linear feedback policy rules which were superior to this consistent rule, typically by a substantial amount." In this article dominant group does not occur but "dominant" does: "dominant player", "dominant firm", and "[f]or policy selection, the policymaker is dominant".

Here a dominant group definition is very similar to the above yet may be

Def. a superior class of [policy or decision] rules is called a dominant group.

These two examples are closer to a genus differentia definition.

A third article is not too different from the first two. Per the following citation: "class" occurs over 100 times in the article and refers to class of stock, as in "superior class of stock", class A shares owned by corporate insiders of top management, class B are the inferior class of stock; "sect" refers again to "section" of the article; "superior" as already indicated; and "rules" refers to takeover rules benefitting the insiders and "voting rules" also benefitting insiders.

Def. a superior class [of stock owned by the corporate insiders] rules [takeover gains and voting for the insiders] is called a dominant group of stock.

Each of the dominant group definitions requires additional words to clarify what's happening; i.e., to make the definition more precise to the specific situations.

Economics five conditions
For rule 1, with the added terms making each definition more precise, each definition succeeds in setting out the essential attributes of the thing defined. The essential attributes for a dominant group are fulfilled by the superior-class-ruling variations.

Rule 2 requires non-circularity, which is arguably accomplished by the relative synonym "superior class" plus "rules".

Rule 3 may not be met in each example because each is specialized and requires the added terms to be precisely applied, yet what the dominant group consists of and what it is ruling (or how it is ruling) must be specified. While the "rules" on the one hand may be considered a "group of rules" or "set of rules". On the other hand, "rules" do rule.

Rule 4 examination of the three definitions suggests some obscurity, especially without the precising terms. Alternate relative synonyms may make the definitions more relevant.

None of the definitions is negative (rule 5).

Hypotheses

 * 1) Dominant group, like volcano, has been around hominins so long that just about everyone has an intuitive meaning for the two-word term.


text:
University of Florida/Egm4313/s12.team6.reports/R1

Problem 1: Spring-dashpot system in parallel with a mass and applied force
Derive the equation of motion of a spring-dashpot system in parallel, with a mass and applied force $$ f(t) $$

Given
Spring-dashpot system in parallel

Solution
The kinematics of the system can be described as,

 * {| style="width:100%" border="0" align="left"

$$\displaystyle x = x_k = x_c $$
 *  $$\longrightarrow(1) $$
 * }
 * }

The kinetics of the system can be described as,

 * {| style="width:100%" border="0" align="left"

$$\displaystyle m\ddot{x} + f_I = f(t) $$ and,
 *  $$\longrightarrow(2) $$
 * }
 * }
 * {| style="width:100%" border="0" align="left"

$$\displaystyle f_I = f_k + f_c $$
 *  $$\longrightarrow(3) $$
 * }
 * }

Given that,

 * {| style="width:100%" border="0" align="left"

$$\displaystyle f_k = kx_k $$
 *  $$\longrightarrow(3a) $$
 * }
 * }

 * {| style="width:100%" border="0" align="left"

$$\displaystyle f_c = c\dot{x_c} $$
 *  $$\longrightarrow(3b) $$
 * }
 * }

From (1), it can be found that, $$\displaystyle \dot{x} = \dot{x_k} = \dot{x_c} $$ and, $$\displaystyle \ddot{x} = \ddot{x_k} = \ddot{x_c} $$

From (3), it can be found that, $$\displaystyle f_I =c\dot{x_c} + kx_k $$

Finally, it can be found that
 * {| style="width:60%" border="0"

$$ m\ddot{x} + c\dot{x} + kx = f(t) $$
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 * style="width:10%; padding:10px; border:2px solid #8888aa" |
 *
 * }
 * }

Author
Solved by: EGM4313.s12.team6.hill 19:05, 1 February 2012 (UTC)

Question
Derive the equation of motion of the spring - mass - dashpot in Fig. 53, in K 2011 p. 85, with an applied force r(t) on the ball.

Solution
There are 2 possible cases that can occur in this problem, depending on the direction of the applied force. In both cases, $$ F_{applied}=r(t) $$ $$ F_{inertia}=my'' $$ $$ F_{damping}=cy' $$ $$ F_{spring}=ky $$

Case 1

The applied force is in the positive direction, and therefore the displacement is in the positive direction.

From the Free Body Diagram, we get the equation

$$ F_{applied}+F_{inertia}-F_{damping}-F_{spring}=0 $$

Rearranging the equation, we get

$$ F_{applied}=-F_{inertia}+F_{spring}+F_{damping} $$

Replacing Force variables, we get

$$ r(t)=my''+cy'+ky $$

Case 2

The applied force is in the negative direction, and therefore the displacement is in the negative direction.

From the Free Body Diagram, we get the equation

$$ -F_{applied}-F_{inertia}+F_{damping}+F_{spring}=0 $$

Rearranging the equation, we get

$$ F_{applied}=-F_{inertia}+F_{spring}+F_{damping} $$

Replacing Force variables, we get

$$ r(t)=my''+cy'+ky $$

Conclusion
Since both cases return the same solution, the equation of motion is derived as:

 * {| style="width:100%" border="0"

$$ r(t)=my''+cy'+ky $$
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 * style="width:20%; padding:10px; border:2px solid #8888aa" |
 *
 * }
 * }

Author
Solved by: Egm4313.s12.team6.hickey 20:04, 1 February 2012 (UTC)

Problem 3: Spring-dashpot-mass system
For the spring-dashpot-mass system on p.1-4, draw the FBDs and derive the equation of motion (2) p.1-4

Given
spring-dashpot-mass system

Solution

The equation of motion
 * $$my''+f_{i}=f(t)$$

where:
 * $$my''$$

is the inertial force
 * $$f_{i}$$

is the internal force
 * $$f(t)$$

is the applied force this analysis assumes:

Assumptions:

 * Motion in the horizontal direction
 * Massless spring
 * Massless dashpot
 * massless connections

Solution:
To analyze the system we look at the kinematics and kinetics of the system Kinematics: This involves the displacement which affects the mass. The displacement, represented by:
 * $$y$$  :    This is the total displacement of the spring plus the displacement of the dashpot.
 * $$y_{k}$$  :     represents the displacement of the spring
 * $$y_{c}$$  :     represents the displacement of the dashpot
 * $$y=y_{k}+y_{c}$$

Kinetics: this involves the forces associated with the displacements. The spring and dashpot are in series, therefore at any section in the series the internal for will be the same. This is denoted as:  $$y_{i}$$. The force in the dashpot is proportional to the first time derivative of displacement (velocity)

 * $$f_{k}=f_{c}=f_{i}=ky_{k}=cy'_{c}$$

Where :  $$k$$   is the spring constant.
 * $$c$$  is the damping coefficient.

and:  $$y'_{c}$$   is the velocity of the dashpot. From this we get :  $$y'_{c}=(k/c)y_{k}$$ which presents :  $$y'_{c}$$   in terms of :   $$y_{k}$$

The constitutive relations: The spring force is equal to the spring constant times the displacement of the spring. The damping force from the dashpot is equal to the damping coefficient times the velocity.
 * $$y=y_{k}+y_{c}$$

this presents two unknown dependent variables by using the relation

 * $$ y=y_{k}+(y_{c}')' $$

Becomes:
 * $$ y=y_{k}+ \frac {k}{k} y_{k}' $$

now we can rewrite the equation of motion:  $$my''+f_{i}=f(t)$$ as :$$ m[yk''+ \frac {k}{c} yk']+fi=f(t) $$ However >:  $$f_{i}=f_{k}$$ so we get: $$m[yk''+ \frac {k}{c} yk']+fk=f(t)$$

 * {| style="width:100%" border="0"

 * style="width:25%; padding:10px; border:2px solid #8888aa" |
 * $$ m[y_{k}''+ \frac {k}{c} y_{k}']+f_{k}=f(t) $$   :
 * $$ m[y_{k}''+ \frac {k}{c} y_{k}']+f_{k}=f(t) $$   :

 *
 * }
 * }

Author
Solved by: Hopeton87 19:42, 1 February 2012 (UTC)

Problem 4: RLC circuit
Derive (3) and (4) from (2) on pg. 2-2

Given:
$$V=LC\frac{d^2V_{c}}{dt^2}+RC\frac{dV_{c}}{dt}+V_{c}$$

Find:
Derive the below two equations from the given:

 * A)     $$LI''+RI'+\frac{1}{C}I=V'$$

 * and

 * B)     $$LQ''+RQ'+\frac{1}{C}Q=V$$

Part A:
From Eq. 2-2(1): $$Q=CV_{c}=\int Idt$$

$$\therefore \frac{dI}{dt}=C\frac{d^2V_{c}}{dt}$$

substituting $$Q=CV_{c}=\int Idt$$ into $$RC\frac{dV_{c}}{dt}$$ we get:   $$RI$$

substituting $$\frac{dI}{dt}=C\frac{d^2V_{c}}{dt}$$ into $$LC\frac{d^2V_{c}}{dt^2}$$ we get:    $$LI'$$

So we now have:   $$V=LI'+RI+V_{c}$$

Deriving the whole equation we get:

 * $$V'=LI''+RI'+\frac{dV_{c}}{dt}$$

by multiplying $$\frac{dV_{c}}{dt}$$ by $$/frac{C}{C}$$ we get:

 * $$V'=LI''+RI'+\frac{CdV_{c}}{Cdt}$$

we can now sub $$Q=CV_{c}=\int Idt$$ for $$\frac{CdV_{c}}{dt}$$ giving us:

Part B:
From Eq. 2-2(1): $$Q=CV_{c}=\int Idt$$

multiplying  $$V_{c}$$   by $$\frac{C}{C}$$ we get $$\frac{CV_{c}}{C}$$

Subbing $$Q=CV_{c}=\int Idt$$ into $$\frac{CV_{c}}{C}$$ we get:

 * $$V=LC\frac{d^2V_{c}}{dt^2}+RC\frac{dV_{c}}{dt}+\frac{Q}{C}$$

taking the first and second derivative of  $$Q=CV_{c}$$   we get:

 * $$Q'=C\frac{dV_{c}}{dt}$$ and $$Q''=C\frac{d^2V_{c}}{dt^2}$$

substitute $$Q'=C\frac{dV_{c}}{dt}$$ into $$RC\frac{dV_{c}}{dt}$$ we get:   $$RQ'$$

substitute $$Q=C\frac{d^2V_{c}}{dt^2}$$ into $$LC\frac{d^2V_{c}}{dt^2}$$ we get:   $$LQ$$

Author
Solved by:Egm4313.s12.team6.mcpherson 19:52, 1 February 2012 (UTC) Egm4313.s12.team6.jagolinzer 19:58, 1 February 2012 (UTC)

Problem 5:
This problem consists of finding a general solution to two linear, second order differential equations with constant coefficients. The problems are taken from the tenth edition of Erwin Kreyszig's Advanced Engineering Mathematics and can be found as problems 4 and 5 of problem set 2.2 on page 59.

Given:
$$y''+6y'+(\pi^2+4)y=0$$

Find:
The homogeneous solution to the differential equation.

Solution:
Use the method of undetermined coefficients, also known as the method of trial solution, to solve the differential equation.

Let   $$y=e^{\lambda x}$$

Therefore:

 * $$y'=\lambda e^{\lambda x}$$
 * and
 * $$y''=\lambda^2 e^{\lambda x}$$

So,
 * $$y''+6y'+(\pi^2+4)y=0$$

can be written as
 * $$e^{\lambda x}(\lambda^2+a\lambda+b)=0$$  where   $$a=6$$   and   $$b=\pi^2+4$$

Since the exponential $$e^{\lambda x}$$ can never equal zero,

 * $$\lambda^2+a\lambda+b=0$$

This equation can be solved for lambda using the quadratic equation :

 * $$\lambda =\frac{-a\pm \sqrt[]{a^2-4b}}{2}$$

Substituting values:

 * $$\lambda =\frac{-(6)\pm \sqrt[]{(6)^2-4(\pi^2+4)}}{2}$$

Which evaluates to:

 * $$\lambda =-3\pm \sqrt[]{-19.478}$$

 * or

 * $$\lambda =-3\pm 2.207i$$

Since the discriminant is less than zero we let $$\omega=2.207$$ and the homogeneous solution will be of the form:

 * $$y=e^{\frac{-ax}{2}}(Acos(\omega x)+Bsin(\omega x))$$

Substituting values we have the homogeneous solution:
 * {| style="width:100%" border="0"

$$y=e^(Acos(2.21 x)+Bsin(2.21 x))$$
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 * style="width:45%; padding:10px; border:2px solid #8888aa" |
 *
 * }
 * }

Given:
$$y''+2\pi y'+\pi^2y=0$$

Find:
The homogeneous solution to the differential equation.

Solution:
Use the method of undetermined coefficients, also known as the method of trial solution, to solve the differential equation.

Let   $$y=e^{\lambda x}$$

Therefore:

 * $$y'=\lambda e^{\lambda x}$$
 * and
 * $$y''=\lambda^2 e^{\lambda x}$$

So,
 * $$y''+2\pi y'+\pi^2y=0$$

can be written as
 * $$e^{\lambda x}(\lambda^2+a\lambda+b)=0$$  where   $$a=2\pi$$ and $$b=\pi^2$$

Since the exponential  $$e^{\lambda x}$$   can never equal zero,

 * $$\lambda^2+a\lambda+b=0$$

This equation can be solved for lambda using the quadratic equation :

 * $$\lambda =\frac{-a\pm \sqrt[]{a^2-4b}}{2}$$

Substituting values we can see that the discriminant is zero:

 * $$\lambda =\frac{-2\pi\pm \sqrt[]{4\pi^2-4\pi^2}}{2}$$

Therefore, only one solution can be found from this equation:

 * $$y_{1}=e^{-\pi x}$$

For the second solution reduction of order must be used:

Let:

 * $$y_{2}=uy_{1}$$

Then,

 * $$y_{2}'=u'y_{1}+y_{1}'u$$

and
 * $$y_{2}=uy_{1}+2u'y_{1}'+y_{1}''u$$

Substituting these into the original equation gives:

 * $$(uy_{1}+2u'y_{1}'+y_{1}u)+a(u'y_{1}+y_{1}'u)+ buy_{1}=0$$

Which simplifies to:
 * $$uy_{1}'+u'(2y_{1}'+ay_{1})+u(y_{1}+ay_{1}'+by_{1})=0$$

Since,

 * $$2y_{1}'=-ae^{\frac{-a}{2}x}=-ay_{1}$$

and
 * $$y_{1}''+ay_{1}'+by_{1}=0$$

What remains is:

 * $$u''y_{1}=0$$

or
 * $$u''=0$$

Therefore,

 * $$u=C_{1}x+C_{2}$$

Now we let  $$C_{1}=1$$   and   $$C_{2}=0$$   so that:

 * $$u=x$$

Now,

 * $$y_{2}=xy_{1}=xe^{-\pi x}$$

Using  $$y_{1}$$   and   $$y_{2}$$   we have the general solution:

 * {| style="width:100%" border="0"

$$y=(C_{1}+C_{2}x)e^{-\pi x}$$
 * style="width:25%; padding:10px; border:2px solid #8888aa" |
 * style="width:25%; padding:10px; border:2px solid #8888aa" |
 *
 * }
 * }

Author
Solved by:EGM4313.s12.team6.davis 02:50, 1 February 2012 (UTC)

Problem 6
For each ODE in Fig.2 in K 2011 p.3 (except the last one involving a system of 2 ODEs), determine the order, linearity (or lack of), and show whether the principle of superposition can be applied.

Given
$$(1) {y}''=g=constant$$

$$(2) m{v}'=mg-bv^{2}$$

$$(3) {h}'=-k\sqrt{h}$$

$$(4) m{y}''+ky=0$$

$$(5) y''+\omega_{0}^2=cos(\omega t)$$,  $$\omega_{0}=\omega$$

$$(6) L{I}''+R{I}'+\frac{1}{c}I={E}'$$

$$(7) EIy^{iv}=\mathit{f(x)}$$

$$(8) \mathit{L{\theta}''+gsin{\theta}=0}$$

Solution
The order of an ODE is found by looking for the highest derivative. If an ODE is linear, than the principle of superposition can be used by finding the solution to the homogeneous equation and finding the particular solution and then adding up the two. If an equation is not linear, then the principle of superposition cannot be applied. $$(1) {y}''=g=constant$$ Order:2nd order. The highest derivative is a 2nd derivative on the y. Linearity:Linear. Superposition:Yes.

$$(2) m{v}'=mg-bv^{2}$$ Order:1st order. The highest derivative is a 1st on the v. Linearity:Non-linear. Superposition:No.

$$(3) {h}'=-k\sqrt{h}$$ Order:1st order Linearity:Non-linear. Superposition:No.

$$(4) m{y}''+ky=0$$ Order:2nd order. Linearity:Linear. Superposition:Yes.

$$(5) y''+\omega_{0}^2=cos(\omega t)$$,  $$\omega_{0}=\omega$$ Order:2nd order Linearity:Linear. Superposition:Yes.

$$(6) L{I}''+R{I}'+\frac{1}{c}I={E}'$$ Order:2nd order Linearity:Linear. Superposition:Yes.

$$(7) EIy^{iv}=\mathit{f(x)}$$ Order:4th oder Linearity:Linear. Superposition:Yes.

$$(8) \mathit{L{\theta}''+gsin{\theta}=0}$$ Order:2nd order Linearity:Non-linear. Superposition:Yes.

Author
Solved by:Egm4313.s12.team6.berthoumieux 02:52, 1 February 2012 (UTC)


text:
User:Egm.4313.s12.team2.bblackwell

Hello

title: User:Egm.4313.s12.team2.bblackwell


text:
User:Egm4313.s12.team4.Lorenzo

Susanna Lorenzo's Wiki Page.

title: User:Egm4313.s12.team4.Lorenzo


text:
University of Florida/Egm4313/s12.team4.Lorenzo/R1

Report 1

Problem Statement
For each ODE in Fig.2 in K 2011 p.3 (except the last one involving a system of 2 ODEs), determine the order, linearity (or lack of), and show whether the principle of superposition can be applied.

Order
The order of an equation is determined by the highest derivative. In this report, the first derivative of the y variable is denoted as y′, and the second derivative is denoted as y′′, and so on. This can be determined upon observation of the equation.

Linearity
An ordinary differential equation (ODE) is considered linear if it can be brought to the form : $$y'+p(x)y=q(x)\!$$

Superposition
Superposition can be applied if when a homogeneous and particular solution of an original equation are added, that they are equivalent to the original equation. In this report, variables with a bar over them represent the addition of the homogeneous and particular solution's same variable. For example:

$$ y_p+y_h=\overline y $$

Given
The following equations were given in the textbook on p. 3 : y''=g=constant \! $$
 * 1.6a - $$

mv'=mg-bv^2 \! $$
 * 1.6b - $$

h'=-k\sqrt{h} \! $$
 * 1.6c - $$

my''+ky=0 \! $$
 * 1.6d - $$

y''+\omega_0^2 y=\cos\omega t, \omega_0 = \omega \! $$
 * 1.6e - $$

LI''+RI'+\frac{1}{C} I=E' \! $$
 * 1.6f - $$

EIy^{\omega}=f(x) \! $$
 * 1.6g - $$

L\theta''+g\sin\theta=0 \! $$
 * 1.6h - $$

1.6a
$$ y''=g=constant \! $$ order: 2nd linear: yes superposition: yes
 * The given equation can be algebraically modified as the following:

 * $$y''=g\!$$

 * It can be split up into the following homogeneous and particular solutions:

 * $$y_{h}''=0\!$$
 * $$y_{p}''=g\!$$

 * Adding the two solutions:

 * $$(y_{h}+y_{p})=\overline{y}''\!$$

 * The solution resembles the original equation, therefore superposition is possible

1.6b
$$ mv'=mg-bv^2 \! $$ order: 1st linear: no superposition: no
 * The given equation can be algebraically modified as the following:

 * $$mv'+bv^2=mg\!$$

 * It can be split up into the following homogeneous and particular solutions:

 * $$mv_{h}'+bv_{h}^2=0\!$$
 * $$mv_{p}'+bv_{p}^2=mg\!$$

 * Adding the two solutions:

 * $$m(v_{h}'+v_{p}')+b(v_{h}^2+v_{p}^2)\not= m\overline{v}'+b(\overline{v}^2)\!$$

 * The solution cannot be algebraically modified to resemble the original equation, and therefore superposition is NOT possible as also proven in the class notes

1.6c
$$ h'=-k\sqrt{h} \! $$ order: 1st linear: no superposition: no
 * The given equation can be algebraically modified as the following:

 * $$h'+k\sqrt{h}=0\!$$

 * It can be split up into the following homogeneous and particular solutions:

 * $$h_{h}'+k\sqrt{h_{h}}=0\!$$
 * $$h_{p}'+k\sqrt{h_{p}}=0\!$$

 * Adding the two solutions:

 * $$(h_{h}'+h_{p}')+k(\sqrt{h_{h}}+\sqrt{h_{p}})\not=\overline{h}'+k\sqrt{\overline {h}}\!$$

 * The solution cannot be algebraically modified to resemble the original equation, and therefore superposition is NOT possible

1.6d
$$ my''+ky=0 \! $$ order: 2nd linear: yes superposition: yes
 * The given equation can be algebraically modified as the following:

 * $$y''+\frac{k}{m}y=0\!$$

 * It can be split up into the following homogeneous and particular solutions:

 * $$y_{h}''+\frac{k}{m}y_{h}=0\!$$
 * $$y_{p}''+\frac{k}{m}y_{p}=0\!$$

 * Adding the two solutions:

 * $$(y_{h}+y_{p})+\frac{k}{m}(y_{h}+y_{p})=\overline{y}''+\frac{k}{m}\overline{y}\!$$

 * The solution resembles the original equation, therefore superposition is possible

1.6e
$$ y''+\omega_0^2 y=\cos\omega t, \omega_0 = \omega \! $$ order: 2nd linear: yes superposition: yes
 * The given equation can be algebraically modified as the following:

 * $$y''+\omega _{o}^{2}y=\cos (\omega t)\!$$

 * It can be split up into the following homogeneous and particular solutions:

 * $$y_{h}''+\omega _{o}^{2}y_{h}=0\!$$
 * $$y_{p}''+\omega _{o}^{2}y_{p}=\cos (\omega t)\!$$

 * Adding the two solutions:

 * $$(y_{h}+y_{p})+\omega _{o}^{2}(y_{h}+y_{p})=\overline{y}''+\omega _{o}^{2}\overline{y}\!$$

 * The solution resembles the original equation, therefore superposition is possible

1.6f
$$ LI''+RI'+\frac{1}{C} I=E' \! $$ order: 2nd linear: yes superposition: yes
 * The given equation can be algebraically modified as the following:

 * $$I''+\frac{R}{L}I'+\frac{1}{LC}I=\frac{E'}{L}\!$$

 * It can be split up into the following homogeneous and particular solutions:

 * $$I_{h}''+\frac{R}{L}I_{h}'+\frac{1}{LC}I_{h}=0\!$$
 * $$I_{p}''+\frac{R}{L}I_{p}'+\frac{1}{LC}I_{p}=\frac{E'}{L}\!$$

 * Adding the two solutions:

 * $$(I_{h}+I_{p})+\frac{R}{L}(I_{h}'+I_{p}')+\frac{1}{LC}(I_{h}+I_{p})=\overline{I}''+\frac{R}{L}\overline{I}'+\frac{1}{LC}\overline{I}\!$$

 * The solution resembles the original equation, therefore superposition is possible

1.6g
$$ EIy=f(x) \! $$ order: 4th linear: yes superposition: yes
 * The given equation can be algebraically modified as the following:

 * $$y-\frac{1}{EI}y=0\!$$

 * It can be split up into the following homogeneous and particular solutions:

 * $$y_{h}-\frac{1}{EI}y_{h}=0\!$$
 * $$y_{p}-\frac{1}{EI}y_{p}=0\!$$

 * Adding the two solutions:

 * $$(y_{h}'+y_{p}')-\frac{1}{EI}(y_{h}+y_{p})=\overline{y}-\frac{1}{EI}\overline{y}\!$$

 * The solution resembles the original equation, therefore superposition is possible

1.6h
$$ L\theta''+g\sin\theta=0 \! $$ order: 2nd linear: no superposition:no
 * The given equation can be algebraically modified as the following:

 * $$\theta''+\frac{g}{L}\sin\theta=0\!$$

 * It can be split up into the following homogeneous and particular solutions:

 * $$\theta_{h}''+\frac{g}{L}\sin\theta_{h}=0\!$$
 * $$\theta_{p}''+\frac{g}{L}\sin\theta_{p}=0\!$$

 * Adding the two solutions:

 * $$(\theta_{h}+\theta_{p})+\frac{g}{L}(\sin\theta_{h}+\sin\theta_{p})\not=\overline{\theta}''+\frac{g}{L}\sin\overline{\theta}\!$$

 * The solution cannot be algebraically modified to resemble the original equation, and therefore superposition is NOT possible


text:
User:Egm4313.s12.team3.chaffee

Statement
Derive the equation of motion of the spring-mass-dashpot in Fig. 53, in Kreyszig 2011 p.85, with an applied force $$f(t)$$ on the ball.

Solution

 * Kinematics:
 * {| style="width:100%" border="0"

$$\displaystyle y=y_c=y_k $$     (2.1)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * Kinetics:
 * {| style="width:100%" border="0"

$$\displaystyle ma+{{f}_{c}}+{{f}_{k}}=f(t) $$     (2.2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * Constitutive relations:
 * {| style="width:100%" border="0"

$$\displaystyle y=y_k=y_c $$     (2.3)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$  \displaystyle {{f}_{k}}=k{{y}_{k}} $$     (2.4)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$  \displaystyle {{f}_{c}}=c{{y}_{c}}' $$     (2.5)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$\displaystyle ma=my'' $$     (2.6)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * Combining equations (2.2-2.6):
 * {| style="width:100%" border="0"

$$\displaystyle my''+c{{y}_{c}}'+k{{y}_{k}}=f(t) $$     (2.7)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$  \displaystyle y=y_k=y_c $$     (2.8)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * Final equation of motion:
 * {| style="width:100%" border="0"

$$ my''+cy'+ky=f(t) $$ (2.9)
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 * style="width:92%; padding:10px; border:2px solid #8888aa" |
 *
 * }

Author
Solved and typed by - --Egm4313.s12.team3.chaffee 11:36, 30 January 2012 (UTC) Reviewed By -

Edited By - --Egm4313.s12.team3.chaffee 00:00, 30 January 2012 (UTC)

Solution

 * Free body diagrams:

From the FBD of the spring, the spring creates a force opposing the direction of motion and the wall must always react in equal magnitude and opposite direction. Summation of the forces in the x-direction leads to:
 * {| style="width:100%" border="0"

$$\displaystyle k{{y}_{k}}=k{{y}_{k}} $$     (3.1) From the FBD of the dashpot, the spring force acts on one side of the dashpot while the damping force acts on the other side. Summation of the forces in the x-direction leads to:
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$\displaystyle f_k=f_c $$     (3.2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$\displaystyle k{{y}_{k}}=cv=c{{y}_{c}}' $$     (3.3) From the FBD of the ball, the dashport force and the inertial forceacts on one side of the ball while the forcing function acts in the opposite direction. Summation of the forces in the x-direction leads to:
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$\displaystyle f(t)=ma+c{{y}_{c}}' $$     (3.4) From the above equations we see that the spring force and damping force are equal and can all be considered internal forces.
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$\displaystyle k{{y}_{k}}=c{{y}_{c}}'=f_{I} $$     (3.5) Knowing that the total displacement is:
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$\displaystyle y={{y}_{k}}+{{y}_{c}} $$     (3.6)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

$$\displaystyle a=y'' $$     (3.7) We can combine equations (3.3), (3.5), and (3.6) to find:
 * style="width:95%" |
 * style="width:95%" |
 *
 * }
 * {| style="width:100%" border="0"

(3.8)
 * $$ my'' + f_{I} = f(t) $$
 *

 *

 * }

Author
Solved and Typed By - Egm4313.s12.team3.chaffee 11:30, 25 January 2012 (UTC)

Reviewed By -

Edited By - --Egm4313.s12.team3.chaffee 15:51, 30 January 2012 (UTC)

title: User:Egm4313.s12.team3.chaffee


text: File:1.3 FBD dashpot.jpg

title: File:1.3 FBD dashpot.jpg


text: File:Q x.png

title: File:Q x.png


text: File:1.3 FBD mass.jpg

title: File:1.3 FBD mass.jpg


text: File:1.3 FBD spring.gif

title: File:1.3 FBD spring.gif


text:
File:Spring-dashpot-ball2.PNG

Licensing
for school project

title: File:Spring-dashpot-ball2.PNG


title: File:R1.3FBD.png


text: File:P x.png

title: File:P x.png


text:
File:Spring-ball-dashpot.PNG

Licensing
for school project

title: File:Spring-ball-dashpot.PNG


text: File:Team11 Report 1 R1.2 Figure 1.jpg

title: File:Team11 Report 1 R1.2 Figure 1.jpg


text:
File:Spring-dashpot-parallel.png

Licensing
for school project

title: File:Spring-dashpot-parallel.png


text: File:Original.jpg

title: File:Original.jpg


text:
User talk:Hopeton87

For the spring dashpot system shown, draw the free body diagram and derive the equation of motion.

Problem 3

The equation of motion
 * $$my''+f_{i}=f(t)$$

where:

 * $$my''$$

is the inertial force

 * $$f_{i}$$

is the internal force

 * $$f(t)$$

is the applied force

this analysis assumes:

Assumptions:

 * Motion in the horizontal direction
 * Massless spring
 * Massless dashpot
 * massless connections

Solution:
To analyze the system we look at the kinematics and kinetics of the system

Kinematics: This involves the displacement which affects the mass. The displacement, represented by:
 * $$y$$  :    This is the total displacement of the spring plus the displacement of the dashpot.
 * $$y_{k}$$  :     represents the displacement of the spring
 * $$y_{c}$$  :     represents the displacement of the dashpot
 * $$y=y_{k}+y_{c}$$

Kinetics: this involves the forces associated with the displacements. The spring and dashpot are in series, therefore at any section in the series the internal for will be the same. This is denoted as:  $$y_{i}$$. The force in the dashpot is proportional to the first time derivative of displacement (velocity)

 * $$f_{k}=f_{c}=f_{i}=ky_{k}=cy'_{c}$$

Where :  $$k$$   is the spring constant.

 * $$c$$  is the damping coefficient.

and:  $$y'_{c}$$   is the velocity of the dashpot. From this we get :  $$y'_{c}=(k/c)y_{k}$$ which presents :  $$y'_{c}$$   in terms of :   $$y_{k}$$

The constitutive relations:

The spring force is equal to the spring constant times the displacement of the spring. The damping force from the dashpot is equal to the damping coefficient times the velocity.
 * $$y=y_{k}+y_{c}$$

this presents two unknown dependent variables by using the relation

 * $$ y=y_{k}+(y_{c}')' $$

Becomes:

 * $$ y=y_{k}+ \frac {k}{k} y_{k}' $$

now we can rewrite the equation of motion: $$my''+f_{i}=f(t)$$

as :$$ m[yk''+ \frac {k}{c} yk']+fi=f(t) $$ However >:  $$f_{i}=f_{k}$$

so we get: $$m[yk''+ \frac {k}{c} yk']+fk=f(t)$$

 * {| style="width:100%" border="0"

 * style="width:25%; padding:10px; border:2px solid #8888aa" |
 * $$ m[y_{k}''+ \frac {k}{c} y_{k}']+f_{k}=f(t) $$   :
 * $$ m[y_{k}''+ \frac {k}{c} y_{k}']+f_{k}=f(t) $$   :

 *
 * }
 * }

title: User talk:Hopeton87


title: File:150854.jpg


text: File:SpringFBD.jpg

title: File:SpringFBD.jpg


text:
File:FBD1 R1.2a.jpg

Licensing
for school project

title: File:FBD1 R1.2a.jpg


text:
User:Egm4313.s12.VoiceofReason

It was just some friendly advice, no need to get all serious and try and track me down.

title: User:Egm4313.s12.VoiceofReason


text: File:DashpotFBD.jpg

title: File:DashpotFBD.jpg


text:
User:Egm6322.s12.sungsik

Problem 8.6
Show that

$$ P_{2k}(x) is even$$

$$ P_{2k+1}(x) is odd$$

where

$$ P_n(x) = \sum^{[n/2]}_{i=0}(-1)^i\frac{(2n-2i)!x^(n-2i)}{2^ni!(n-i)!(n-2i)!} $$

Even Function $$ F(x) = -F(x) $$

Odd Function $$ F(x) = F(-x) $$

When n=2k

$$ P_{2k}(x) = \sum^{[2k/2]}_{i=0}(-1)^i\frac{(4k-2i)!x^(2k-2i)}{2^2ki!(2k-i)!(2k-2i)!} $$

above equation, x term is the factor to deciede even or odd function.

Therefore, extract x term and expand it

Let assume that k = 5

Then, equation is reduced below

$$\sum_{i=0}^{[5]}x^{10-2i}= x^{10} + x^8 + x^6 + x^4 + x^2 + x^0 $$

since 6 terms are even functions, therefore, $$ P_{2k} $$ is even function

when n=2k+1

$$ P_{2k+1}(x) = \sum^{[2k+1/2]}_{i=0}(-1)^i\frac{(2(2k+1)-2i)!x^{((2k+1)-2i)}}{2^(2k+1)i!(2k+1)-i)!((2k+1)-2i)!} $$

extract x term and expand it

Assuming k=5

$$\sum_{i=0}^{[5]}x^{11-2i}= x^{11} + x^9 + x^7 + x^5 + x^3 + x^1 $$

Since those terms are odd function, therefore, $$P_{2k+1} $$ is odd function

title: User:Egm6322.s12.sungsik


text: File:MassFBD.jpg

title: File:MassFBD.jpg


text:
User:Egm4313.s12.team14.pickett.report1

R1.5

Given:
 * {| style="width:100%" border="0" align="left"

{y}'' + 4{y}' + ({\pi}^2 + 4)y = 0, $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 1)
 * }
 * }

Problem: Find the general solution for this homogeneous differential equation.

Solution: Assume that the solution is of the form
 * {| style="width:100%" border="0" align="left"

y_h = e^{\lambda x} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 2)
 * }
 * }

 * {| style="width:100%" border="0" align="left"

\therefore y'_h = \lambda e^{\lambda x} $$ $$ And
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 3)
 * }
 * }

 * {| style="width:100%" border="0" align="left"

y''_h = \lambda^2 e^{\lambda x} $$ $$
 * $$\displaystyle
 * $$\displaystyle
 * $$\displaystyle (Eq. 4)
 * }
 * }

Substituting equations 2, 3, and 4 into equation 1 yields

$$\displaystyle \lambda^2 e^{\lambda x} + 4\lambda e^{\lambda x} + (\pi^2 + 4)e^{\lambda x} = 0$$ $$\displaystyle e^{\lambda x}(\lambda^2 + 4\lambda +(\pi^2 + 4)) = 0$$ Since $$\displaystyle e^{\lambda x} \neq 0$$ $$\displaystyle (\lambda^2 + 4\lambda +(\pi^2 + 4)) = 0$$

We must use the quadratic formula to obtain values for lambda $$\displaystyle \lambda = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ $$\displaystyle \lambda = \frac{-4 \pm \sqrt{(4)^2 - 4(1)(\pi^2 + 4)}}{2(1)}$$ $$\displaystyle \lambda = \frac{-4 \pm \sqrt{16 - 4\pi^2 - 16)}}{2}$$ $$\displaystyle \lambda = \frac{-4 \pm \sqrt{-4\pi^2)}}{2}$$ $$\displaystyle \lambda = -2 \pm i{\pi}$$

A solution of the form $$\displaystyle y_h = e^{\lambda z}$$ where z is a complex number of the form $$\displaystyle a + ib$$ requires the use of Euler's Formula, where $$\displaystyle e^{\lambda z} = e^{a}(\cos{b} + i\sin{b})$$

$$\displaystyle \therefore y_{h1} = e^{-2x}(\cos{\pi x} + i\sin{\pi x})$$ $$\displaystyle y_{h2} = e^{-2x}(\cos{-\pi x} + i\sin{-\pi x})$$ Finally $$\displaystyle y_h = C_1[e^{-2x}(\cos{\pi x} + i\sin{\pi x})] + C_2[e^{-2x}(\cos{-\pi x} + i\sin{-\pi x})]$$

R1.6

(A) Falling Stone (y represents height above the ground) $$\displaystyle y'' = g $$ This governing equation is SECOND order and LINEAR

To prove whether the principle of superposition applies to the differential equation, we will suppose that there exists two independent solutions. One solution for the homogeneous case would have any forcing function set to zero, while the particular solution would take the forcing function into account. $$\displaystyle y_{h} $$ $$\displaystyle y_{p} $$ Plugging these two solutions into the equation, we obtain $$\displaystyle {y_h}'' = 0 $$ $$\displaystyle {y_p}'' = g $$ Adding these equations together, we obtain $$\displaystyle {y_h} + {y_p} = g $$

We can see that $$\displaystyle {y_h} + {y_p} = (y_h + y_p)'' $$, which proves that superposition is applicable to this linear differential equation.

(H) Pendulum (theta represents the angle with respect to vertical) $$\displaystyle L{\theta}'' + g{\sin(\theta)} = 0 $$ This governing equation is SECOND order and NON-LINEAR

$$\displaystyle y_{h} $$ $$\displaystyle y_{p} $$ Plugging these two solutions into the equation, we obtain $$\displaystyle L{{\theta}_h}'' + g{\sin({\theta}_h)} = 0 $$ $$\displaystyle L{{\theta}_p}'' + g{\sin({\theta}_p)} = 0 $$ Adding these equations together, we obtain $$\displaystyle L{{\theta}_p} + L{{\theta}_h} + g{\sin({\theta}_p)} + g{\sin({\theta}_h)} = 0 $$

If we plug in a linear combination of the particular and homogeneous solutions into the differential equation, we obtain $$\displaystyle L({\theta}_p +{\theta}_h)'' + g{\sin({\theta}_p + {\theta}_h)} = 0 $$ We can see that $$\displaystyle L({\theta}_p +{\theta}_h) + g{\sin({\theta}_p + {\theta}_h)} \neq L{{\theta}_p} + L{{\theta}_h}'' + g{\sin({\theta}_p)} + g{\sin({\theta}_h)} $$

Therefore the principle of superposition does not hold for this non-linear differential equation.

title: User:Egm4313.s12.team14.pickett.report1