Figure $5\mathrm{.}29$ System for Eumple $5\mathrm{.}12$ with transtational and rotational elemerts.

th te sydem stown in Migure $5\mathrm{.}29,$ the mans and spring are connected to the disk by a fecribie cable. Acraally, the spring might be used to represent the strenching of the cable. The mass $M$ is subjected to the extermal force $f(l)$ in additice to the gravitational force. Let $$ and $x$ be measured from references corresponding to the position where the shaft $K_1$ is not twisted and the spring $K_2$ is not strectiod. Find the state$-$variable model, treating force in the cabie as outputs.