Calculating Fourier Series for an Odd Function

ganondorf29
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Homework Statement



f(t) is given as:

from 0 to 0.2s, f(t) = 5
from 0.2s to 0.6s, f(t) = 0
from 0.6s to 0.8s, f(t) = 5,
etc

Homework Equations


for an odd function

a0 = 2/p * integral(from -p/2 to p/2) of f(t) dt

bn = 4/p * integral(from 0 to p/2) of f(t)*sin(2*pi*n*t/p) dt

The Attempt at a Solution



The problem is that since the function is "off" for a longer period than it is "on"; I'm not sure how to incorporate that into the Fourier Series, especially the bn term
 
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The function f(t) is neither odd nor even, so you have to use the general formulas for the coefficients, both the a's and b's.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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