Suppose you have the following circuit. The switch has been open for a long time, and is closed at time t = 0.
Assume V2 = 5V, R2 = 10 kΩ, L2 = 2mH, C2 = 0.1µF
The second order differential equation for the voltage across the capacitor is
d^2Vc(t)/dt + a1dVc(t)/dt + a2Vc = K
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