# Extra Credit-discrete Fourier transform

1. Oct 17, 2012

### intelwanderer

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