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Math Help - Laplace transform

  1. #1
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    Laplace transform

    Could someone show me how to do the following Laplace transform?

    f(t) =
    e^(2t) if 0 < t < 8
    1 if t > 8

    F(s) = ?

    I'm pretty lost. Thanks for any help.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by PvtBillPilgrim View Post
    Could someone show me how to do the following Laplace transform?

    f(t) =
    e^(2t) if 0 < t < 8
    1 if t > 8

    F(s) = ?

    I'm pretty lost. Thanks for any help.
    Well we can do thus using just the definition of the Laplace Transform:

    <br />
(\mathcal{L} f) (s) = \int_0^{\infty} f(t) e^{-st} dt <br />
= \int_0^8 e^{2t}e^{-st} dt + \int_8^{\infty} e^{-st}dt<br />
= \int_0^8 e^{t(2-s)} dt + \int_8^{\infty} e^{-st}dt<br />

    ........ =\frac{1}{s-2}[1-e^{8(2-s)}] + \frac{e^{-8s}}{s}

    RonL
    Last edited by CaptainBlack; May 25th 2007 at 03:30 PM.
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  3. #3
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    Makes sense.
    Thank you very much.
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