Initial conditions set as Q = 50*C Coulomb, I = 0.
time t ranges from 0.00 through 0.04 seconds
vertical scale runs from -100 to 100 Volts.
black line shows voltage across capacitor, q/C.
red line shows voltage across resistor, i R = q' R
green line shows voltage across inductor, i' L = q'' L
this is the solution to the RLC series circuit:
q'' + (R/L)q' + q/(LC) = 0
or to the free damped harmonic oscillator
x'' + (c/m)x' + kx/m = 0