(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

f(t) is an odd, periodic function with period 1 and:

f(t) = -5.5 + 22*t^{2}for -0.5 ≤ t < 0

i) find the Fourier coefficient bn

ii) find the Fourier coefficient b5

2. Relevant equations

bn = (2/T) * ∫ f(t) *sin((2*n*∏*t)/T) dt between T/2 and -T/2

sin(n*∏) = 0 for all values of n

cos(n*∏) = 1 for even values of n

cos(n*∏) = -1 for odd values of n

3. The attempt at a solution

by integrating f(t)*sin((2*n*∏*t)/T) with respect to t i get:

-(11*sin(n*∏) - 11*n*∏*cos(n*∏))/(n^3 * ∏^3)

replacing the sin(n*∏) with 0 i get:

11*cos(n*∏))/(n^2 * ∏^2)

so this should be the solution to the first part of the question but when i put n into the equation as 5, i get the wrong answer. can anyone see where ive gone wrong?

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# Fourier Series Problem

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