# Damping coefficient

by mlee
Tags: coefficient, damping
 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
 Sci Advisor HW Helper PF Gold P: 12,016 How should Newton's 2.law of motion look like?
 P: 25 i think it is: -kx-bv=ma
 Sci Advisor HW Helper PF Gold P: 12,016 Damping coefficient That's correct! Now, what type of solutions have you learnt that this differential equation has?
 HW Helper P: 2,277 See it as $$-kx - b \frac{dx}{dt} = m\frac{d^2 x}{dt^2}$$
 HW Helper P: 2,277 You're right, thanks alridno
 P: 25 v= dx/dt and a= d^2/dt^2
 P: 25 but what is the answer of d^2/dt^2 then?
 Sci Advisor HW Helper PF Gold P: 12,016 mlee: Any progress at what sort of solutions your equation has?
 P: 25 uh not really...;(
 Sci Advisor HW Helper PF Gold P: 12,016 Now, I'd like you try a solution of the form: $$x(t)=Ae^{rt}$$ (A and r constants) What condition must be placed on "r" in order for this to be a solution. Please post your work.
 P: 25 Asin(wt)+Bcos (wt)
HW Helper
PF Gold
P: 12,016
 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.
 P: 25 Ae-bt/2mCos(ω't + φ)
 P: 25 Ae^(bt/2m)*cos(w't+φ)
 Sci Advisor HW Helper PF Gold P: 12,016 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 $$A,\phi$$ Besides, what is your value of "w"?
 P: 25 ω = sqrt(k/m) ω' = √((k/m) - (b²/4m²))
 Sci Advisor HW Helper PF Gold P: 12,016 Now, so how does your initial conditions determine $$A,\phi$$?

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