Can anyone help me out with this?(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Problem with a Fourier Series

**Physics Forums | Science Articles, Homework Help, Discussion**