Homework Help: Fourier Series

1. Jan 28, 2010

Physics197

1. The problem statement, all variables and given/known data

Find the Fourier series for: sin(a*pi*t). Consider what happens when a -> 1/L

2. Relevant equations

3. The attempt at a solution

I keep getting zeros for a_o, a_n, and b_n.

I though that atleast b_n should give me something, can anyone also confirm this?

2. Jan 28, 2010

LCKurtz

What is L? Are you trying to find an expansion on (-L,L) using terms like $\sin{(n\pi x/l)}$ And are you assuming in your calculations that a is an integer? If a is not an integer you should get lots of bn terms. Make sure you haven't assumed that terms like $\sin{a\pi}$ are zero in your calculations. Hard to guess without seeing your work.

3. Jan 28, 2010

Physics197

Sorry for wasting your time, but I didn't feel like typing up a page of work.

4. Jan 28, 2010

LCKurtz

It might not be wasting either of our times. A common mistake students make when, for example, trying to find the fourier series for sin(3x) on $(-\pi,\pi)$ is to think the forumla for

$$b_n=\frac 1 \pi \int_{-\pi}^\pi \sin{(3x)}\sin{(nx)}\ dx$$

works when n = 3, which it doesn't. So they are puzzled why all the bn are zero. Your question made me think you might be making one or both that type of error or assuming a is an integer.

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