Results 1 to 3 of 3

Math Help - Fourier Sine Series Exapnsion

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    23

    Fourier Sine Series Exapnsion

    The question ask to expand the following function of period 2L on the interval (0,L) as a Fourier sine series.

    \[f(x)=sin(\frac{\pi}{2L}x)\]<br />

    This function is periodic on a period of 4L and thus the coefficients are given by

    \[b_{n}=\frac{1}{2L}\int_{0}^{2L}sin(\frac{\pi x}{2L})sin(\frac{n\pi x}{2L})dx\]<br />

    Upon evaluating the integral, I split the sine terms into two seperate cosine terms using a trig identity. After integration I am unable to get a single cosine as given in the correct answer

    \[f(x)=\frac{8}{\pi}\sum_{n=1}^{\infty}\frac{ncos(n\  pi)}{1-4n^{2}}sin(\frac{n\pi}{L}x)\]<br />

    Have I made an error or am I on the correct track?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by dats13 View Post
    The question ask to expand the following function of period 2L on the interval (0,L) as a Fourier sine series.

    \[f(x)=sin(\frac{\pi}{2L}x)\]<br />

    This function is periodic on a period of 4L and thus the coefficients are given by

    \[b_{n}=\frac{1}{2L}\int_{0}^{2L}sin(\frac{\pi x}{2L})sin(\frac{n\pi x}{2L})dx\]<br />
    Because the integrand is not periodic with period 2L you have to integrate over -L,L here, also you divide by 2L in the second sin term and you should not it should just be L. You could also do this the way shown in the MathWorld page.

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2010
    Posts
    23
    Thanks, for pointing out my mistake. I got the correct answer now.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Sine and Cosine Fourier series
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 26th 2010, 07:48 AM
  2. Fourier sine and cosine series of x(Pi-x)
    Posted in the Advanced Applied Math Forum
    Replies: 3
    Last Post: January 2nd 2010, 12:42 PM
  3. PDE-fourier sine series (help!!!)
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: May 14th 2009, 05:17 AM
  4. is this a sine or cosine fourier series...
    Posted in the Advanced Math Topics Forum
    Replies: 1
    Last Post: February 14th 2009, 04:04 PM
  5. Fourier sine series...
    Posted in the Calculus Forum
    Replies: 5
    Last Post: February 10th 2008, 07:53 AM

Search Tags


/mathhelpforum @mathhelpforum