A circuit is constructed with a resistor, two inductors, one capacitor, one battery and a switch as shown. The value of the resistance is R, 184 \Omega. The values for the inductances are: $L_1$ = 236 mH and $L_2$ = 166 mH. The capacitance is C = 157 \mu F and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a sign.
1) The switch has been closed for a long time when at time t = 0, the switch is opened. What is $U_L(0)$, the magnitude of the energy stored in inductor $L_1$ just after the switch is opened?
2) What is \omega_\text{res}, the resonant frequency of the circuit just after the switch is opened?
3) What is $Q_\text{max}$, the magnitude of the maximum charge on the capacitor after the switch is opened?
4) What is Q(t_1), the charge on the capacitor at time $t_1$ = 3.42 ms. Q(t_1) is defined to be positive if V(a) - V(b) is positive.
5) What is $t_2$, the first time after the switch is opened that the energy stored in the capacitor is a maximum?
6) What is the total energy stored in the inductors plus the capacitor at time $t = t_2$?
