# Fourier series (Whats wrong?)

• May 16th 2013, 08:52 PM
Brennox
Fourier series (Whats wrong?)
I keep getting these answers wrong, which part is wrong id love some help.

For mathqs1......Q2 i have also tried 18 and 27

For mathqs2..... Q5 i have also tried 0

• May 16th 2013, 11:14 PM
zzephod
Re: Fourier series (Whats wrong?)
Quote:

Originally Posted by Brennox
I keep getting these answers wrong, which part is wrong id love some help.

For mathqs1......Q2 i have also tried 18 and 27

For mathqs2..... Q5 i have also tried 0

For $\displaystyle S_2(x)$ you should enter a formula something like $\displaystyle a+b \sin(x) + c \cos(x) + d \sin(2x) + e \cos(2x)$ where $\displaystyle a,b,c,d,e$ are numerical values you have calculated from the function and Fourier series definitions.

.
• May 16th 2013, 11:24 PM
zzephod
Re: Fourier series (Whats wrong?)
Quote:

Originally Posted by Brennox
I keep getting these answers wrong, which part is wrong id love some help.

For mathqs1......Q2 i have also tried 18 and 27

For mathqs2..... Q5 i have also tried 0

For question 5 you want to evaluate:

$\displaystyle a_n=\frac{1}{\pi}\int_{-\pi}^{\pi}f(t) \cos(nt)\;dt = \frac{2}{\pi} \int_{0}^{\pi}f(t) \cos(n t)\;dt$

The last term is because $\displaystyle f(t)$ is the even extension of $\displaystyle f(t)$ defined on $\displaystyle (0,\pi)$.

.
• May 17th 2013, 01:17 AM
Brennox
Re: Fourier series (Whats wrong?)
Quote:

Originally Posted by zzephod
For $\displaystyle S_2(x)$ you should enter a formula something like $\displaystyle a+b \sin(x) + c \cos(x) + d \sin(2x) + e \cos(2x)$ where $\displaystyle a,b,c,d,e$ are numerical values you have calculated from the function and Fourier series definitions.

.

yeah i did that but got the wrong answer can you try it?
• May 17th 2013, 07:19 AM
zzephod
Re: Fourier series (Whats wrong?)
Quote:

Originally Posted by Brennox
yeah i did that but got the wrong answer can you try it?

$\displaystyle a_n=\frac{1}{\pi}\int_{-\pi/2}^{\pi/2}9\times \cos(nt)\;dt=\frac{18\,\sin\left( \frac{\pi\,n}{2}\right) }{\pi\,n}$

which can be simplified further, and because you have an even function all $\displaystyle b_n=0$