1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Fourier Series Help

  1. Apr 15, 2006 #1
    Can anyone help me out with this?

    Find the steady state periodic solution of the following differential equation.

    x''+10x= F(t), where F(t) is the even function of period 4 such that
    F(t)=3 if 0<t<1 , F(t)=-3 if 1<t<2.

    Im basically just having a problem findind the general Fourier series for F(t).
    I know how to do the latter part of the problem.

    My work so far: Knowing this is even, I can eliminate the sin part of the fourier series. So in general I need to solve for the series cofficients of a(0) and a(n)

    for a(o) I get 0. Which makes sense too, even just by inspection of the graph of the function.

    My problem is with a(n). My final result is [6/npi]*[sin(npi/2)]. How do I express that second term in my answer. I noticed that the sign alternates every other odd number. a(n) =0 for every even number.

    Thanks a bunch
  2. jcsd
  3. Apr 15, 2006 #2
    My new basis of thought is that the a(n) Fourier coefficient can only be positive 6/npi... is this correct... if figure when you add the negative term, the coefficient becomes zero again. At no point can it be negative.

    Correct me if I am wrong.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook