Damping coefficient

1. mlee

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

2. arildno

12,015
How should Newton's 2.law of motion look like?

3. mlee

25
i think it is:
-kx-bv=ma

4. arildno

12,015
That's correct!
Now, what type of solutions have you learnt that this differential equation has?

5. Pyrrhus

2,276
See it as

$$-kx - b \frac{dx}{dt} = m\frac{d^2 x}{dt^2}$$

Last edited: Oct 9, 2004
6. Pyrrhus

2,276
You're right, thanks alridno

7. mlee

25
v= dx/dt and a= d^2/dt^2

8. mlee

25
but what is the answer of d^2/dt^2 then?

9. arildno

12,015
mlee:
Any progress at what sort of solutions your equation has?

10. mlee

25
uh not really...;(

11. arildno

12,015
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.

12. mlee

25
Asin(wt)+Bcos (wt)

13. arildno

12,015
This is a solution of an UNDAMPED, harmonic oscillator.
Your oscillator is NOT undamped; try my approach, and post your work.

14. mlee

25
Ae-bt/2mCos(ω't + φ)

15. mlee

25
Ae^(bt/2m)*cos(w't+φ)

16. arildno

12,015
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"?

17. mlee

25
ω = sqrt(k/m)
ω' = √((k/m) - (b²/4m²))

18. arildno

12,015
Now, so how does your initial conditions determine $$A,\phi$$?

19. mlee

25
i dunno how to find $$phi$$

20. mlee

25
and w' = 5*10^2-(b^2/1*10^-2)
is that right?