The uniform solid cylinder of mass m and radius r rolls without slipping during its osci...

The uniform solid cylinder of mass m and radius r rolls without slipping during its oscillation on the circular surface of radius R. If the motion is confined to small amplitudes determine the period of the oscillations. Also determine the angular velocity ω of the cylinder as it crosses the vertical centerline. (Caution: Do not confuse used in the defining equations. Note also that θ is not the angular displacement of the cylinder.)