$($a$).$ The parameters of a spring mass damper system are $m=b=k=2$ units. For a value of proportional gain $Kp=16$ the system becomes critically damped. Find the closed loop stiffness and $(4)$ the corresponding derivative gain Kv for a position regulator system that maintains the position of

$($b$)$ The parameters of a spring, mass, damper system are $m=b=k=1$ unit. Find $,,Kp$ and $Kv$ for a position regulator control law $($employing the partitioned control method$)$ that results in the system being critically damped with a closed loop stiffness of $16\mathrm{.}0$

Q$8.$ Consider an image $\text{'}$ I $\text{'}$ and