damping coefficient

mlee

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

arildno

How should Newton's 2.law of motion look like?

mlee

i think it is:
-kx-bv=ma

arildno

That's correct!
Now, what type of solutions have you learnt that this differential equation has?

Pyrrhus

See it as

[tex] -kx - b \frac{dx}{dt} = m\frac{d^2 x}{dt^2} [/tex]

Pyrrhus

You're right, thanks alridno

mlee

v= dx/dt and a= d^2/dt^2

mlee

but what is the answer of d^2/dt^2 then?

arildno

mlee:
Any progress at what sort of solutions your equation has?

mlee

uh not really...;(

arildno

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

Asin(wt)+Bcos (wt)

arildno

This is a solution of an UNDAMPED, harmonic oscillator.
Your oscillator is NOT undamped; try my approach, and post your work.

mlee

Ae-bt/2mCos(ω't + φ)

mlee

Ae^(bt/2m)*cos(w't+φ)

arildno

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

ω = sqrt(k/m)
ω' = √((k/m) - (b²/4m²))