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Math Help - Period of function

  1. #1
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    Period of function

    Considering the function u(t,x)=\sum_{h=1}^{\infty}\left(a_{n}\cos\frac{n\p  i}{L}ct+b_{n}\sin\frac{n\pi}{L}ct\right)\sin\frac{  n\pi}{L}x

    I know that the period of this function is 2\pi/L, but I am not sure how to prove it. I tried plugging in the period for t and reducing, but didn't get very far. Is this the right approach? Can anyone help with this?

    Thanks in advance!
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  2. #2
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    If your period is T, then u(t+T,x) = u(t,x) for all t and x.
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  3. #3
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    Quote Originally Posted by snowtea View Post
    If your period is T, then u(t+T,x) = u(t,x) for all t and x.

    Actually, if \displaystyle T is the period, then \displaystyle u(t+kT,x) = u(t,x), for any integer, \displaystyle k.

    So, you need to show that \displaystyle T is the smallest value for which \displaystyle u(t+T,x) = u(t,x) is true.
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