# Harmonic motion

1. Apr 15, 2005

### ness9660

Im really not sure how to solve this. For the oscillations themself the angular frequency is w=sqrt(k/m)? Although this is not going to be the angular frequency of the cylinder. Im looking through my book and all my notes, I really cant figure out how to relate the angular frequency of the wheel to the oscillations.

for this problem Ive been trying to use w=sqrt((m*g*d)/I).
Im not sure if Im on the right track, as Im not sure what to use for d and Im still trying to calculate the moment of inertia. Am I correct in assuming that I is the sum of the moments of inertia on each side of the axis? So that you would have I =(1/2)(9.7)(1.326^2) + (1/2)(9.7)(2.57^2)?

thanks for any help.

2. Apr 15, 2005

### learningphysics

For a simple spring oscillator we can derive the frequency from the energy equation:

$$E=\frac{1}{2}kx^2 + \frac{1}{2}mv^2$$

This equation leads to a frequency of $$\sqrt{\frac{k}{m}}$$

Try to find a similar equation for total energy of your cylinder oscillator.... you have the energy stored in the spring... the translational kinetic energy of the cylinder.... and the rotational kinetic energy of the cylinder. When you get the equation in the same form as the above equation.... you should be able to get frequency.

Hint: what is the relationship between w (angular velocity) and v (linear velocity) when the cylinder does not slip.