(Solved): 8.8 In the circuit shown in Figure P8.8, FIGURE P8.8 a. write a differential equation in \( v(t) \) ...

8.8 In the circuit shown in Figure P8.8, FIGURE P8.8 a. write a differential equation in \( v(t) \). b. find \( \alpha \) and \( \omega_{0} \). c. find the characteristic equation. d. find the roots of the characteristic equation. e. find the voltage \( v(t) \) across the capacitor for \( t \geq 0 \) and plot \( v(t) \). f. find the current \( i(t) \) for \( t \geq 0 \) and plot \( i(t) \).