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

[zedmondson033]

Homework Statement

Solve the following forced D.E. (Show work)

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

Homework Equations

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

L(d²x/dt²)+R(dx/dt)+x/C=200sin(t)

The Attempt at a Solution

y=y_general+y_particular

I calculated y_general to be y_general = 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!

 

[Bohrok]

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

 

[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.

 

[ehild]

I calculated y_general to be y_general = 10e^-tcos(3t)+(10/3)e^-tsin(3t)

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