$(2^4|{|}^4.$ For the electromechanical system shown in Figese $2$

$($a$)$ Write all the necesseny equations to draw the bleck diagam of the system. $(10$ pis$)$

$($b$)$ Draw the bleck diegrem of the system with

J$.$ When the system shiown in Figues $3$ is subjected to a unit step input, the system respond with an underdamped response having an ovastiot of $16\mathrm{.}3\%$ and perk time $T_p=3\mathrm{.}142$ see. Determine