(Solved): *5. a) Consider the circuit shown in the Figure below. First find a differential equation model for ...

*5. a) Consider the circuit shown in the Figure below. First find a differential equation model for the output, $$v_2(t)$$. Then derive a state space representation for the above circuit assuming the state variables to be: $${\mathrm{x}}_1(\mathrm{t})=$$ Voltage across capacitance, $${\mathrm{C}}_1$$. $${\mathrm{x}}_2(\mathrm{t})=$$ Current through the inductor, $${\mathrm{L}}_1$$ b) Assuming $${\mathrm{R}}_1={\mathrm{R}}_2=1?,{\mathrm{C}}_1=1\mathrm{F}$$, and $${\mathrm{L}}_1=1\mathrm{H}$$, find the transfer function, $$\mathrm{G}(\mathrm{s})={\mathrm{V}}_2(\mathrm{s})/{\mathrm{V}}_1(\mathrm{s})$$, from the above state space representation,