$5\mathrm{.}16$ Figure P$5\mathrm{.}16$ shows the $2-$DOF single$-$mass mechanical system from Problem $2\mathrm{.}9$ in Chapter $2.$ Note that the series connection of the damper and spring is reversed from Problem $5\mathrm{.}15.$

Figure P$5\mathrm{.}16$

a$.$ Obtain an SSR of this mechanical system where $\backslash ($ z$\_\{1\}\backslash )$ is the output and the applied force, $\backslash ($ f$\_\{$a$\}($t$)\backslash )$ is the input.

b$.$ Derive the I$/$O equation for the system.