Question

Can you please solve this question using clear detailed steps and indicating the part number next to each and every answer please? Thank you!

PS: WILL GIVE A THUMBS UP FOR THE CLEAREST CORRECT ANSWER :)

(1 point) This problem concerns the electric circuit shown in the figure below. Capacitor Resistor Inductor A charged capacitor connected to an inductor causes a current to flow through the inductor until the capacitor is fully discharged. The current in the inductor, in turn, charges up the capacitor until the capacitor is fully charged again. If Q(t) is the charge on the capacitor at time t, and I is the current, then dQ dt If the circuit resistance is zero, then the charge Q and the current / in the circuit satisty the differential equation dt C where C is the capacitance and L is the inductance, so Then, just as as a spring can have a damping force which affects its motion, so can a circuit; this is introduced by the resistor, so that if the resistance of the resistor is R,

CONT OF QUESTION:

Answer 1

Given that The electric circuit is Given differential equation is L d^2Q/dt^2 + R dQ/dt + 1/c Q = 0 L = 1, R = 2/3 dQ/dt C = 9 d^2Q/dt^2 + 2/3 dQ/dt + 1/9 Q = 0 Auxiliary equation is m^2 + 2/3 m + 1/a = 0 (m + 1/3)^2 = 0 m = -1/3, 1/3 Qeuro = (c_1 + c_2 t) e^- t/3 = (c_1 + c_2) e^- t/3 rightarrow (1) \r\n Q' (t) = -c_1/3 e^- t/3 - c_2/3 e^- t/3 (t - 3) rightarrow (2) Q (0) = 0 and a' (0) = 2 Q (0) = 0 Substitute Q (0) in equation 1 we get