$5.$ The feedback control system shown below is given by:

a$.(2$ points$)$ What type of compensation is shown in the system above?

b$.(1$ point$)$ What is the time constant of the sensor$?$

c$.(2$ points$)$ What type of filter is the plant?

d$.(10$ points$)$ Find ALL the gains, $\backslash ($ K $\backslash ),$ that will make the closed loop system critically damped.