$(10$ points$)$ The transfer function of a simplified DC motor model is:

$\frac{(s)}{V(s)}=\frac{C_{\text{t}\text{o}\text{r}}}{K_{\text{e}\text{m}\text{f}}{C}_{\text{t}\text{o}\text{r}}+B{R}_a+J_a{R}_{a}s}$

where $C_{\text{t}\text{o}\text{r}}$ is the torque constant, $K_{\text{e}\text{m}\text{f}}$ is the back EMF constant, the load rotation is resisted by a torsional damper $B,J_a$ is the equivalent inertia at the armature, and $R_a$ is the armature resistance.

With a unit$-$step input, find a$)$ the D$.$C$.$ gain of the system, b$)$ the steady$-$state response, and c$)$ the time when the system response reaches $63\mathrm{.}2\%$ of the final value.