1. The problem statement, all variables and given/known data 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. 2. Relevant equations 3. 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?