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Creating Fourier sine Series

  1. Mar 3, 2016 #1

    RJLiberator

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    1. The problem statement, all variables and given/known data

    Find the Fourier series for the following function (0 ≤ x ≤ L):
    y(x) = Ax(L-x)

    2. Relevant equations


    3. The attempt at a solution

    1. We start with the sum from n to infinity of A_n*sin(n*pi*x/L) where An = B_n*Ax(l-x)

    2. We have the integral from 0 to L of f(x)*sin(m*pi*x/L) dx

    I really have no idea what to do, I am francticlly looking through notes and websites. I understand the Fourier sine series should be pretty easy to find, it's just plugging in values, but there are so many different equations/elements.

    Let me try this solution:

    f(x) = L/pi(sum from n = 1 to infinity of sin(n*pi*x/L)

    Ah?
     
  2. jcsd
  3. Mar 3, 2016 #2

    DrClaude

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    When you are asked the for the Fourier series of a function, your answer should be the coefficients appearing in the sum.
     
  4. Mar 3, 2016 #3

    RJLiberator

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    From my notes, would:

    A_m = 2/L integral from 0 to L f(x)*sin(m*pi*x/L) dx be the answer then?

    where f(x) = Ax(L-X)
     
  5. Mar 3, 2016 #4

    RJLiberator

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    Okay, let me say this:

    We start with the Fourier Since series:
    sum from 1 to infinity of (b_n*sin(n*pi*x/L))

    where b_n = 2/L integral from 0 to L (f(x)*sin(n*pi*x/L))

    where f(x) = the function in question, namely Ax(L-x)

    All together we have

    The sum from n=1 to infinity of 2/L integral from 0 to L of (Ax(L-x))*sin^2(n*pi*x/L) dx
     
  6. Mar 3, 2016 #5

    DrClaude

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    While formally correct, this doesn't answer the question. You have to find an expression for the b_n.
     
  7. Mar 3, 2016 #6

    RJLiberator

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    b_n = 2/L integral from 0 to L (f(x)*sin(n*pi*x/L))
    where f(x) = the function in question, namely Ax(L-x)

    so b_n = 2/L integral from 0 to L (Ax(L-x)*sin(n*pi*x/L))
    Is that incorrect for b_n?
     
  8. Mar 3, 2016 #7

    DrClaude

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    It's a start. Now you have to perform the integral.
     
  9. Mar 3, 2016 #8

    vela

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    Now that you've been working with Fourier series for a while, it wouldn't hurt to go back and review the derivation of the various formulas (using one reference). If you understand the basics, all the variations/conventions will make more sense and won't seem so confusing.
     
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