$5\mathrm{.}2.$ For each system shown in Fig. $5\mathrm{.}24$:

$($a$)$ Draw the linear graph.

$($b$)$ Determine the system order and identify a set of state variables.

$($c$)$ Derive the state equations and express them in matrix form.

$($d$)$ Write the output equation for the velocity of the mass $v_m.$

Figure $5\mathrm{.}24$: Two mechanical systems.