please solve till the end. and solve handwritten. not with AI$.$

The angular velocity co$($t$)$ of a rotor is governed by the following equation: $J_{{}^{}}(t)+B_{}(t)=T(t)$

Here, $J$ is the moment of inertia of the rotor, $B$ is the coefficient of the equivalent viscous friction that represents all the dissipative effects, and $T(t)$ is the controlling torque.

For a desired speed $(t)={}_0(t)h(t),T(t)$ serated according to the proportional control law

a$)$ Draw the block diagram representation of the closed$-$loop system.

c$)$ It is desired to improve its steady state error $(t).$ integral time parameter $T_T.$ Obtain the state accuracy by adding integral control action with an control action added.

the steady state value $({}_s)$ of the error $(t)$ when integral steady state value. Explain mathematically oscillatory behaviour in this case before reaching its

e$)$ Determine the limit $T_i($ in terms of $J^{\text{'}}B$ why it may do so$.$ oscillatory behaviour if $T_i>T_i.$