A closed loop system has the following block diagram:

a$)$ Determine the transfer function between $Y(s)$ and $R(s),$ where $Y(s)=L\{y(t)\}$ and $R(s)$

$=L\{r(t)\}$

b$)$ Find the value of $K$ that will give the fastest non$-$oscillatory response in $Y(s)$ to a step

change in $R(s).$

c$)$ What is the corresponding ODE that relates $r(t)$ to $y(t)?$