Q$1.$ Characteristics for the Servo problem is given as:

$G_p(s)=\frac{1}{s^2+4s+1}$;$,G_c(s)=K_c$;$,G_m(s)=G_f(s)=1$

Estimate the values of Kc yield

a$)$ Over$-$damped

b$)$ Critically damped

c$)$ Under$-$damped closed$-$loop responses.

d$)$ Show the block diagram and plot the response graph for the each closed$-$loop system $($over$-$damped, critically damped, and under$-$damped$)$ if a unit step is applied by using Simulink. Show also the offset value by using the graph.

e$)$ Discuss the stability of this system.