For what value of d is the frequency of small oscillations largest?

[Tonyt88]

Homework Statement

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?

Homework Equations

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

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

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.

 

[Tonyt88]

Add on:

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?

 

[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.