# Homework Help: For what value of d is the frequency of small oscillations largest?

1. Dec 13, 2006

### Tonyt88

1. The problem statement, all variables and given/known data
A coin of radius R is pivoted at a point that is distance d from the center. The coin is free to swing back and forth in the vertical plane defined by the plane of the coin. For what value of d is the frequency of small oscillations largest?

2. Relevant equations

Frequency = 1/T = (1/2(pi))(k/m)^1/2

x = A cos( (omega)(t) + phi )

3. The attempt at a solution

I assume I have to find some derivative in order to maximize the value, just don't know where to start.

2. Dec 13, 2006

### Tonyt88

Would this be correct?

F = ma in the tangental direction

-mg sin(theta) = ma

-mg sin(theta) = m((R+d) theta '' ) (note theta '' is 2nd derivative)

thus omega = (g/(R+d))^1/2

Or is this totally the wrong idea?

3. Dec 14, 2006

### Meir Achuz

You have to use the moment of inertia of a disk, and then use the parallel axis theorem so that you can apply torque=I alpha to the coin.