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Fourier Series Problem

  1. Oct 30, 2007 #1
    1. The problem statement, all variables and given/known data

    Consider F(t) = sin(wt) when 0 < t < pi/w and 0 when pi/w < t < 2pi/w. Where w is the frequency and t is the time. Find the Fourier Series

    2. Relevant equations


    F(t) = sum of (ck e^ikt)

    See attached doc with math type; its a lot more readable.

    3. The attempt at a solution


    ck = (w/2pi integral from 0 to pi/w of sin(wt)*e^-ikx) + (w/2pi integral from pi/w to 2pi/w of sin(wt)*e^-ikx)

    I’m not sure how to do this integration. If all the trig functions had the same argument, it would be do-able, but they don’t. w is a constant, right? And k isn’t, right? :confused: We never dealt with stuff like this back in calc. I’m very grateful for any help or suggestions. I tried to use trig addition formulas, but that didn’t work. Thanks! :smile:
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Oct 30, 2007 #2

    Meir Achuz

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    Science Advisor
    Homework Helper
    Gold Member

    Your integral is over t, not x, so it should have exp(-ikt).
    Write sin(wt) as [exp(iwt)-exp(-iwt)]/2i, and do the exponential integrals.
     
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