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Extra Credit-discrete Fourier transform

  1. Oct 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Show that the normal coordinates for the equation we derived in Problem Set 4, Problem 2 are given by the discrete Fourier transform of an infinite series and the eigenfrequencies corresponding to each k.

    http://www.ph.utexas.edu/~asimha/PHY315/Solutions-4.pdf [Broken]

    The solution to the problem we are solving for is given above-Problem 2

    q'' = ω(2qj - qj+1 - qj-1)


    2. Relevant equations

    I'd assume we'd use the infinite Fourier transform given in the problem statement.

    Ʃexp(2∏ijk)q(t) from j = negative∞ to ∞

    That's all I can think of at the moment.


    3. The attempt at a solution

    OK, this is an extra credit problem, so naturally, it's harder than the rest of the HW. We don't have to use this kind of math on a regular basis, hence I'm more than a little lost on how to get started. I went with this over the TA weeks ago(I was curious on how you got the real solution), but was too dumb to write down what he said. I'm sure if I got a little help, I'll remember...
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
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