1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

  1. Aug 10, 2011 #1
    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. jcsd
  3. Aug 10, 2011 #2
    You'll need to find the particular solution before you can plug in the initial conditions to find the constants.
     
  4. Aug 10, 2011 #3
    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.
     
  5. Aug 10, 2011 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    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
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Solving a 2nd order D.E. of a forced LRC circuit
  1. 2nd Order D.E. help (Replies: 5)

  2. 2nd order d.e (Replies: 2)

Loading...