In Figure, assume that the cylinder rolls without slipping. The spring is at its free length when

Question:

In Figure, assume that the cylinder rolls without slipping. The spring is at its free length when x and y are zero,
(a) Derive the equation of motion in terms of x, with y(t) as the input,
(b) Suppose that m = 10 kg, R = 0.3 m, k = 1000 N/m, and that y(t) is a unit-step function. Solve for x(t) if x(0) =(0) = 0.