Finding Fourier Series of sin(a*pi*t): Results & Confirmation

[Physics197]

Homework Statement

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

Homework Equations

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?

 

[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 b_n 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.

 

[Physics197]

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

 

[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 formula 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 b_n are zero. Your question made me think you might be making one or both that type of error or assuming a is an integer.