Chapter 4, Problem 4.23P

In Figure P4.23, 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 $y\left(t\right)$ as the input. (b) Suppose that $m=10$ kg, $R=0.3$ m, $k=1000$ N/m, and that $y\left(t\right)$ is a unit-step function. Solve for $x\left(t\right)$ if $x\left(0\right)=\stackrel{\dot{}}{x}\left(0\right)=0$ .