Problem $22\mathrm{.}1\mathrm{.}2$

Consider the three$-$mass, three$-$spring systems shown in Fig. $22\mathrm{.}6\mathrm{.}2.$ Determine equations of motion for these systems using generalized coordinates corresponding to the displacement of each mass. You may express your answer as either three individual $($coupled$)$ equations or as a $33$ matrix equation.

Figure $22\mathrm{.}6\mathrm{.}2$: Three blocks on a frictionless surface held together with springs.