I need to use a L-R-C tank in my design and I'm having trouble with the calculations. And I think it is because of the phase shift I didn't take into account.
Here you can see there is a differential equation introduced to extract the current-wave-charge equation. To my calculations the frequency is correct but I also need to know the phase shift \$ \theta \$ as well.
This is supposed to be the voltage wave of my LRC circuit:
ww = 660.764; vc = 30; slip = 0.99; result =
Cos[ww*t]*
vc*(Exp[-t*((0.461 + (ww*slip)*
ww*1715.38/(66564 +
6648.72*(ww*
slip)^2))/(2*(134*10^-5 + (5420 + (ww*
slip)^2*5.385)/(66564 +
6648.72*(ww*slip)^2))))]); Plot[result, {t, 0, Pi/ww}]
However, as you can see, the cosine wave is slightly shifted and it messes with my further calculations. So, what is the equation for the phase shift \$ \theta \$ ?
simulate this circuit – Schematic created using CircuitLab
I added the example schematic. In the initial condition, VC is 30V. Then I showed the graph of VC. VC is charged up to 30V in initial state and then slowly dies.
This above graph is taken from circuit lab simulation of the circuit above. This is the correct waveform with no phase shift because the simulator included the phase shift into equation. How can I so?