Problem $1$:

For the circuit shown in the below Figure, the input is a voltage source $v_i(t)$ and the output is the voltage across the capacitor $v_0(t).$ Use a state variable model to describe the circuit.

$($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 $T(s)=Vo\frac{s}{V_i}(s)$

$L=0\mathrm{.}1H,R=4,C=0\mathrm{.}01F$