(Solved): must sketch relevant circuits, graphs ,phasors and all signals that are changing with time  2.2 ...

2.27 There is no energy stored in the circuit shown in Fig. P12.27 at the time the switch is opened. a) Derive the integrodifferential equation that governs the behavior of the voltage \( v_{0} \). b) Show that \[ V_{o}(s)=\frac{I_{\mathrm{dc}} / C}{s^{2}+(1 / R C) s+(1 / L C)} . \] c) Show that \[ I_{o}(s)=\frac{s I_{\mathrm{dc}}}{s^{2}+(1 / R C) s+(1 / L C)} . \] Figure P12.27