Transient Circuit Simulation and Time Domain Response for the Capacitor Voltage in an RLC series circuit.
Watch the derivation of the 2nd order equation first: https://youtu.be/84rxZAg0090
Watch the solution of a RLC series circuit with R=1k, L=2H, C=0.5F. next:
https://youtu.be/wELyPmiPUgc
