So we've been working on a RLC circuit, where the subject is oscillations. We accomplished to work out a differential equation, for this specific circuit, however solving it is a completely other part of the problem. We're completely stuck here and hopefully, there are some of you, who could help us move on :)
The equation is as following, using Kirchoffs law of the sum of the currents in a closed circuit:
(d^2v/dt) L + (dv/dt)R + (1/C)v = 0
We tried looking at the general solution, where we did find a complex solution. Looking at the real part, we get equation which looks like:
k * e^-(α/2βt)sinw0(t).
where k, α and β are constants, here our R, L and C values. However, we just can't seem to find the solution, where our constants are included. In other words, how to determine k, α and β as R, L and C.
Also, searching at the internet, we found that w0 is:
w0 = 1/Sqrt(LC)
But how do you solve w0? Or simply just find the expression for it?