Problem $3$:

Use a state variable model to describe the circuit shown in the below figure.

$($a$)$ Develop the state equations and determine the matrices $A,B,C,D$

$($b$)$ Using the matrices, $A,B,C,D,$ obtain the transfer function $T(s)=V_0\frac{s}{V_1}(s)$

$L=0\mathrm{.}5H,R=5,C=0\mathrm{.}02F$