# Periodic Motion question

1. Apr 8, 2005

### jaymode

Here is my problem:
A hard-boiled egg of mass 45.0 g moves on the end of a spring with force constant k = 24.7 N/m. Its initial displacement is 0.290 m. A damping force F = - bv acts on the egg, and the amplitude of the motion decreases to 0.120 m in a time of 5.10 s.

I need to find the magnitude of the dampening constant b.

I am completely clueless on how to approach this question.

edit: corrected some stuff.

Last edited: Apr 8, 2005
2. Apr 8, 2005

### e(ho0n3

Me too, since I do not know what you mean by 'the force of B'.

3. Apr 8, 2005

### jaymode

sorry i guess i typed it wrong. the dampening force:

F = -bv

I need to find the magnitude of the dampening constant b.

4. Apr 8, 2005

### stunner5000pt

$$x(t) = x_{m} e^{\frac{-bt}{2m}} cos( \omega t)$$

where Xm is the initial displacement
b is hte damping force
m is the mass
omega is the angular frequency $$\omega = \frac{2 \pi}{T}$$ where $$T = 2 \pi \sqrt{\frac{m}{k}}$$

5. Apr 8, 2005

### jaymode

for some reason that is not working for me.

6. Apr 8, 2005

### stunner5000pt

perhaps you are not using your numbers correctly

initla displacement Xm = 0.290 m
k = 24.7 N/m
X(5.10) = 0.120 m
t = 5.10s
m = 45g = 0.045 kg
and omega = $\sqrt{\frac{m}{k}}$
it's blind substitution, really