Question

A cylinder of radius r and mass m rests on a curved path of radius R as shown in Fig. Show that the cylinder can oscillate about the bottom position when displaced and left to itself. Find the period of oscillation. Assume that the cylinder rolls with out slipping.

Answer 1

Restoring torque acting on cylinder after a small displacement θ, about an axis through point of constant O with the curved path,

Angular acceleration of cylinder,