Solve Series RLC Circuit: Kirchhoff's Loop Rule

[Ataman]

Given a series RLC Circuit driven by a generator, Kirchhoff's Loop Rule gives:

$$V_{peak} cos \omega t - L\frac{di}{dt} - IR - \frac{Q}{C} = 0$$

- OR -

$$V_{peak} cos \omega t = L\frac{d^{2}Q}{dt^{2}} + \frac{dQ}{dt}R + \frac{Q}{C}$$

I have never done second order differential equations, so right now I am stuck if I want to solve for Q(t) or I(t).

-Ataman

 

[bitrex]

I've just started studying differential equations, but this seems like a case where you could use the method of homogeneous and particular solutions, where you first find any solution that satisfies the differential equation (the particular solution), then find the homogeneous solution by setting the left side equal to zero and finding some general form (like Ae^st) that also satisfies the equation, and then summing the two. Unfortunately I'm not good enough to actually implement the solution for your problem, so hopefully there is someone else here that could expand on that or show a better way.