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

f(t)= -1 if -∏ < t ≤ 0

1 if 0 < t ≤ ∏

f(t+2∏) = f(t)

question asks to compute first 3 non-zero terms in Fourier series expansion of f(t)

2. Relevant equations

3. The attempt at a solution

since this is an odd function i used the fourier sine series formula

f(t)=

∞

Ʃ (bn) sin(nwt)

n=1

(bn)= (2/L)*

L

∫ f(t)sin(nwt)

0

this is just integral from 0 to L cause i dont know how to use the subscipts on the forum

i got L=∏ since the period,T=2∏

w=1

so my (bn)=(-2/n∏) [cos(n∏)-1]

so as a refult my fourier expansion becomes (bn) sin(nwt)

and i get (-2/n∏) [cos(n∏)sin(nt) - sin(nt)]

and whatever n value i get cos(n∏)=1 so it will be 0 for every n value. im pretty sure i did something wrong here since the answer is

4/∏ [sin(t) + 1/3sin(3t) + 1/5sin(5t)]

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Fourier Series Expansion

**Physics Forums | Science Articles, Homework Help, Discussion**