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Damping coefficient

by mlee
Tags: coefficient, damping
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mlee
#1
Oct9-04, 09:36 AM
P: 25
A 50.0-g hard-boiled egg moves on the end of a spring with force constant . It is released with an amplitude 0.300 m. A damping force acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m.Calculate the magnitude of the damping coefficient . Express the magnitude of the damping coefficient numerically in kilograms per second, to three significant figures

pls who can help me?
thanx
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arildno
#2
Oct9-04, 10:46 AM
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How should Newton's 2.law of motion look like?
mlee
#3
Oct9-04, 10:54 AM
P: 25
i think it is:
-kx-bv=ma

arildno
#4
Oct9-04, 11:32 AM
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Damping coefficient

That's correct!
Now, what type of solutions have you learnt that this differential equation has?
Pyrrhus
#5
Oct9-04, 11:55 AM
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See it as

[tex] -kx - b \frac{dx}{dt} = m\frac{d^2 x}{dt^2} [/tex]
Pyrrhus
#6
Oct9-04, 12:05 PM
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You're right, thanks alridno
mlee
#7
Oct9-04, 12:06 PM
P: 25
v= dx/dt and a= d^2/dt^2
mlee
#8
Oct9-04, 12:08 PM
P: 25
but what is the answer of d^2/dt^2 then?
arildno
#9
Oct9-04, 12:08 PM
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mlee:
Any progress at what sort of solutions your equation has?
mlee
#10
Oct9-04, 12:12 PM
P: 25
uh not really...;(
arildno
#11
Oct9-04, 12:14 PM
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Now, I'd like you try a solution of the form:
[tex]x(t)=Ae^{rt}[/tex] (A and r constants)
What condition must be placed on "r" in order for this to be a solution.
Please post your work.
mlee
#12
Oct9-04, 12:27 PM
P: 25
Asin(wt)+Bcos (wt)
arildno
#13
Oct9-04, 12:29 PM
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Quote Quote by mlee
Asin(wt)+Bcos (wt)
This is a solution of an UNDAMPED, harmonic oscillator.
Your oscillator is NOT undamped; try my approach, and post your work.
mlee
#14
Oct9-04, 03:06 PM
P: 25
Ae-bt/2mCos(ω't + φ)
mlee
#15
Oct9-04, 03:08 PM
P: 25
Ae^(bt/2m)*cos(w't+φ)
arildno
#16
Oct9-04, 03:10 PM
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You lack a minus sign in your exponential!
Now, knowing
a) The initial displacement
and
b)That the initial velocity is zero
How can you determine [tex]A,\phi[/tex]

Besides, what is your value of "w"?
mlee
#17
Oct9-04, 03:21 PM
P: 25
ω = sqrt(k/m)
ω' = √((k/m) - (bē/4mē))
arildno
#18
Oct9-04, 03:26 PM
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Now, so how does your initial conditions determine [tex]A,\phi[/tex]?


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