(a) Write the state equations
$$$\begin{bmatrix}{\dot X}_1\\{\dot X}_2\\{\dot X}_3\end{bmatrix}\;=\;A\;\begin{bmatrix}X_1\\X_2\\X_3\end{bmatrix}\;+\;B\left[e\left(t\right)\right]$$$(b) If e(t) = 0, t $$\geq$$ 0, $$i_{L1}\left(0\right)\;=\;0,\;v_{C2}\left(0\right)\;=\;0,\;i_{L3}\left(0\right)\;=\;1A,$$ then what would the total energy dissipated in the registors in the interval $$\left(0,\infty\right)$$ be
(a) Find the impedance to the right of $$\left( {A,\,\,\,\,\,\,B} \right)$$ at $$\omega \,\,\, = \,\,\,\,0$$ rad/sec and $$\omega \,\,\, = \,\,\,\,\infty $$ rad/sec.
(b) If $$\omega \,\,\, = \,\,\,\,{\omega _0}$$ rad/sec and $${i_1}\left( t \right) = \,\,{\rm I}\,\,\,\sin \,\left( {{\omega _0}t} \right)\,{\rm A},$$ where $${\rm I}$$ is positive, $${{\omega _0}\,\, \ne \,\,0}$$, $${{\omega _0}\,\, \ne \,\,\infty }$$, then find $${\rm I}$$, $${{\omega _0}}$$ and $${i_2}\left( t \right)$$