The switch in Figure P7-42 has been open for a long time and is closed at \(t=0\). The circuit parameters are \(L=\) \(400 \mathrm{mH}, C=0.1 \mu \mathrm{F}, R_{1}=22 \mathrm{k} \Omega, R_{2}=330 \Omega\), and \(V_{\mathrm{A}}=15 \mathrm{~V}\).

(a) Find \(v_{\mathrm{C}}(t)\) and \(i_{\mathrm{L}}(t)\) for \(t \geq 0\).
(b) What is \(\zeta\) for this circuit?
(c) Use Multisim to validate your results. Hint: In Grapher View plot \(v_{\mathrm{C}}(t)\) using the left axis and \(i_{\mathrm{L}}(t)\) on the right axis.
(d) Change the appropriate \(R\) to create the critically damped case.

R ww 1=0 VA R L le m + vc(t) L(1) C