Use the data of Fig.(a). The current i in the circuit of Fig.(b) is

The circuit of Fig. represents a

For the circuit in Fig., write the state equations using v_c and i_L as state variables.

For the circuit in Fig.

(a) Find the Thevenin equivalent of the sub circuit faced by the capacitor across the terminals a, b.

(b) Find $$v_c\left(t\right),\;t>0,\;given\;v_c(0)\;=\;0.$$

(c) Find i(t), t>0.