$2\mathrm{.}2$ Figure P$2\mathrm{.}2$ shows a mechanical system driven by the displacement of the left end, $x_{in}(t),$ which could be

supplied by a rotating cam and follower. When displacements $x_{in}(t)=0$ and $x=0,$ the spring $k$ is neither

compressed nor stretched. Derive the mathematical model of the mechanical system.

Figure P$2\mathrm{.}2$