# Damping coefficient

1. Oct 9, 2004

### 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

2. Oct 9, 2004

### arildno

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

3. Oct 9, 2004

### mlee

i think it is:
-kx-bv=ma

4. Oct 9, 2004

### arildno

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

5. Oct 9, 2004

### Pyrrhus

See it as

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

Last edited: Oct 9, 2004
6. Oct 9, 2004

### Pyrrhus

You're right, thanks alridno

7. Oct 9, 2004

### mlee

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

8. Oct 9, 2004

### mlee

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

9. Oct 9, 2004

### arildno

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

10. Oct 9, 2004

### mlee

uh not really...;(

11. Oct 9, 2004

### arildno

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. Oct 9, 2004

### mlee

Asin(wt)+Bcos (wt)

13. Oct 9, 2004

### arildno

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

14. Oct 9, 2004

### mlee

Ae-bt/2mCos(ω't + φ)

15. Oct 9, 2004

### mlee

Ae^(bt/2m)*cos(w't+φ)

16. Oct 9, 2004

### arildno

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. Oct 9, 2004

### mlee

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

18. Oct 9, 2004

### arildno

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

19. Oct 9, 2004

### mlee

i dunno how to find $$phi$$

20. Oct 9, 2004

### mlee

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