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Math Help - Laplace Transform of Period Square Wave Function

  1. #1
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    Laplace Transform of Period Square Wave Function

    I'm having trouble setting up my equation.

    Square wave with period T = 2a.
    f(t) = 2, 0<t<a
    f(t) = 0, a<t<2a

    Take the Laplace Transform of f(t).

    What I got:

    F(s) = (∫2exp(-st)dt [0,a]) / [1 - exp(-2as)]

    The square brackets [0,a] are the limits of the definite integral.

    Thanks guys.
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  2. #2
    MHF Contributor chisigma's Avatar
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    If f(t) has period T, then its Laplace transform is...

    F(s)= \mathcal{L} \{f(t)\}= \frac{\int_{0}^{T} e^{-st}\cdot f(t)\cdot dt}{1-e^{-sT}} (1)

    In Your case is T=2a and the integral in (1) is...

    \int_{0}^{a} 2\cdot e^{-st}\cdot dt (2)

    ... that is easy to solve...

    Kind regards

    \chi \sigma
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  3. #3
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    Perfect, thank you very much, good to know I was on the right track!
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