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Homework Help: Half-Range Fourier Series

  1. Dec 30, 2008 #1
    1. The problem statement, all variables and given/known data

    Question: Find the half-range Fourier sine series for the function f(t) = t sin(t)

    Problem: According to all the examples I have gone through, they all have a limit when asking for the half-range. However, my teacher, in the question posted above, has not specified any limits. Is this a typing error? If not, can you please nudge me in the right direction.

    2. Relevant equations



    3. The attempt at a solution

    None yet. I'm under the impression that question may have been typed wrong.
     
  2. jcsd
  3. Dec 30, 2008 #2
    I think -pi to pi are standard ...
    Currently, it is an even function, I can suggest making it odd t*cos(t) and finding fourier series from 0 to 2pi.
     
  4. Dec 30, 2008 #3
    Ok here is what I gather so far:

    I am looking for the sine half-series, which is bn.Sin(nt) from the fourier series.

    So,

    bn = I{t.sin(t).sin(nt)} between 0 and 2pi

    ... which goes to ...

    bn = I{t.sint(1+n)} between 0 and 2pi?

    Is that correct?

    EDIT: ... which gives me 0. I think I misunderstood.

    Reading your suggestion again, you have changed t.sin(t) to t.cos(t)... Why is that? I can see we get an odd function (odd . even) but not sure how we came about the change...

    Apologies in advance if I sound retarded, but 2 lectures on fourier was no way near enough in my opinion.
     
    Last edited: Dec 30, 2008
  5. Jan 5, 2009 #4
    Any ideas?
     
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