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 θ = θ₀, determine the period τ of the oscillations. Also determine the angular velocity w of the cylinder as it crosses the vertical centerline. (Caution: Do not confuse w with θ˙ or with w_n as used in the defining equations. Note also that θ is not the angular displacement of the cylinder.)

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