$5\mathrm{.}16$ Figure P$5\mathrm{.}16$ shows the $2-$DOF single$-$mass mechanical system from Problem $2\mathrm{.}5$ 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 position of the mass is the system output and the

applied force is the input.

b$.$ Derive the I$/$O equation using the $D-$operator method. Show that the I$/$O equations $($and hence transfer

functions$)$ for the systems shown in Figs. P$5\mathrm{.}15$ and P$5\mathrm{.}16$ are identical. Hence, either series connection

of the damper or spring results in the same system dynamics.