Period of small oscillation of sphere rolling in cylinder

A solid sphere is rolling without slipping on a vertical circular ramp with radius R. The sphere has radius r and mass m with a moment of inertia I = (2/5)m r^2. Find the period of a small amplitude oscillation.

(See attached file for full problem description with diagram and equations)


Solution Summary

A sphere rolls without slipping on a cylindrical ramp. Period of small oscillations calculated.