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## Homework Statement

A solid sphere (radius = R) rolls without slipping in a

cylindrical trough (radius = 5R), as shown in Figure

P13.56. Show that, for small displacements from equilib-

rium perpendicular to the length of the trough, the

sphere executes simple harmonic motion with a period

T = 2Pi √28R/5g.

## Homework Equations

## The Attempt at a Solution

It's essentially a pendulum type problem except a ball is rolling instead of just moving. Once we get w were set:

Using physical pendulum, w = root(mgd/I):

d = distance to CM of system = 5R-R = 4R = CM of ball.

I = I was thinking that the axis of rotation is at 4R from the CM of the ball, Icm of ball = 2/5MR^2, so I was thinking I = 2/5MR^2 + M(4R)^2, but this doesn't look like it's going to put me in the right direction.

Any thoughts?