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Changing periods. Very confusing

  1. Nov 24, 2006 #1
    This is driving me nuts:

    How do you show that that's true?!? How do you prove it? For the life of me I can't see how this holds despite the fact that I've wasted the past two hours working at it. I can't think of a technical explanation for it (a proof) OR an intuitive one... Please help.
  2. jcsd
  3. Nov 24, 2006 #2


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    It's simple

    [tex] f\left(\frac{Lt}{\pi}+2L\right)=f\left(\frac{L}{\pi}(t+2\pi)\right)=f\left(\frac{L}{\pi}t\right) [/tex]

    So you can see very clearly that if you denote by

    [tex] g(t)=f\left(\frac{L}{\pi}t\right) [/tex]

    , then g has a period of 2\pi.

  4. Nov 24, 2006 #3

    To prove it just show that g(t) = g(t+2pi) using the definition of g and the properties of f.
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