# Solving a 2nd order D.E. of a forced LRC circuit

1. Aug 10, 2011

### zedmondson033

1. The problem statement, all variables and given/known data
Solve the following forced D.E. (Show work)

L=10 R=20 C=0.01 x(0)=10 x'(0)=0

2. Relevant equations
This is the second order D.E. for a forced LRC circuit

L(d2x/dt2)+R(dx/dt)+x/C=200sin(t)

3. The attempt at a solution
y=ygeneral+yparticular

I calculated ygeneral to be ygeneral = e-tC1cos(3t)+e-tC2sin(3t)

Now I need to find the particular solution for the DE. I've been trying to use undetermined coefficients, choosing Asin(t)+Bcos(t) as my initial guess but the algebra doesn't seem to work out. Can anyone help me out? Thanks for your time!

Last edited: Aug 10, 2011
2. Aug 10, 2011

### Bohrok

You'll need to find the particular solution before you can plug in the initial conditions to find the constants.

3. Aug 10, 2011

### zedmondson033

Yeah, the previous problem was to find the solution to the same equation, just without the forcing function at the end, so it was homogeneous. That's how I got the values for the constants and the general equation.

4. Aug 10, 2011

### ehild

This is not the general solution of the homogeneous equation: It has to contain two undetermined constants.

The "force" function has different frequency from the own frequency of the LCR circuit: so the particular solution is in the form A cos(t) +Bsin(t), as you supposed. Find A and B. Show what you have tried.
Match the general solution x(homogeneous) +x(particular) to the initial conditions.

ehild