Q$1$

$($a$)$ Name any two parameters that can be used in the analysis of control systems. Consider the closed loop system shown in the figure below

$($b$)$ Assuming that $g_m^{\text{'}}(s)=1,$ obtain the closed loop characteristics polynomial of the system and hence or otherwise determine the range of values of $K_c$ for the system to closed loop stable.

$($c$)$ With $K_c=2,$ obtained the closed loop transfer function $J(S)=y\frac{S}{r}(S).$ Obtain the unit step response of $y(t).$