The uniform cylinder of mass m and radius R rolls without slipping on the inclined surface...

The uniform cylinder of mass m and radius R rolls without slipping on the inclined surface. The spring with constant k wraps around the cylinder as it rolls.

Determine the equation of motion for the cylinder using the energy method. Determine the numerical value of the period of oscillation of the cylinder using k = 30 N/m, m = 10 kg, R = 30 cm, and θ = 20°.

Figure P9.24