his problem concerns the electric circuit shown in the figure below.CapacitorResistorInductorwwwA charged capacitor connected to an inductor causes a current to flow through the inductor until the capacitor is fully discharged. The current in theinductor, 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,thenI =dQdtIf the circuit resistance is zero, then the charge Q and the current / in the circuit satisfy the differential equationdIL + = 0,dtwhere C is the capacitance and L is the inductance, soLd² Qdt2+= 0.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 ofthe resistor is R,d² QL+ Rdt²dQdt1+== 0.If L = 1 henry, R = ohm, and C = 9 farads, find a formula for the charge when(a) Q(0) = 0 and Q'(0) = 2:Q(t) =(b) Q(0)= 2 and Q'(0) = 0:Q(t) =

To solve the differential equation with initial conditions and , we can assume a solution of the…

Inductor A charged capacitor connected to an inductor causes a current to flow through the inductor until the capacitor is fully discharged. The nductor, 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, an Chen 1 = dQ dt f the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation dl + dt = 0, C where C is the capacitance and L is the inductance, so L 20 = 0.

Inductor A charged capacitor connected to an inductor causes a current to flow through the inductor until the capacitor is fully discharged. The nductor, 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, an Chen 1 = dQ dt f the circuit resistance is zero, then the charge Q and the current I in the circuit satisfy the differential equation dl + dt = 0, C where C is the capacitance and L is the inductance, so L 20 = 0.