Consider the RLC electrical circuit given below, where the input is current \(i_{1}(t)\) and the output is voltage \(v_{o}(t)\).

(a) Find the State-Variable model \((A, B, C, D)\) for the circuit.

(b) Show that the input-output differential equation is given by

\[C \ddot{v}_{o}+\frac{1}{R} \dot{v}_{o}+\frac{1}{L} v_{o}=\dot{i}(t)\]

C R L eee An RLC Electrical Circuit