- #1
kiwifruit
- 8
- 0
Homework Statement
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)
Homework Equations
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 don't 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. I am pretty sure i did something wrong here since the answer is
4/∏ [sin(t) + 1/3sin(3t) + 1/5sin(5t)]