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Math Help - Laplace Transform?

  1. #1
    Member zangestu888's Avatar
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    Laplace Transform?

    Ned help with Laplace transform not sure what to do but have a idea

    the question is find the Laplace transform of;
    te^{\text{-t}}cos(3t) i think u gotta apply the therom (-1)^nd^n/ds^n[F(s)]
    meaning it wil be the dervitive of the transform e^{\text{-t}}cos(3t) am i close :P lol
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    Quote Originally Posted by zangestu888 View Post
    Ned help with Laplace transform not sure what to do but have a idea

    the question is find the Laplace transform of;
    te^{\text{-t}}cos(3t) i think u gotta apply the therom (-1)^nd^n/ds^n[F(s)]
    meaning it wil be the dervitive of the transform e^{\text{-t}}cos(3t) am i close :P lol

    Yes that's correct, and to work out \mathcal{L}\left\{e^{-t} \cos{3t}\right\}

    you need to use \mathcal{L}\left\{e^{\lambda t}f(t)\right\} = \bar{f}\left(p-\lambda\right)

    and \mathcal{L}\left\{ f(\mu t) \right\} = \frac{1}{\mu}\bar{f}\left(\frac{p}{\mu}\right)

    Good luck.
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  3. #3
    Member zangestu888's Avatar
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    can i use the first shifting therom for <br /> <br />
\mathcal{L}\left\{e^{-t} \cos{3t}\right\}<br />
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    Quote Originally Posted by pomp View Post
    to work out \mathcal{L}\left\{e^{-t} \cos{3t}\right\}

    you need to use \mathcal{L}\left\{e^{\lambda t}f(t)\right\} = \bar{f}\left(p-\lambda\right)
    yep.
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  5. #5
    Member zangestu888's Avatar
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    thanks my final answer i got was

    (s^2+4s-8)/(s^2+2s+10)^2 can anyone please verify my transform? thank! you
    Last edited by zangestu888; July 14th 2009 at 03:57 PM.
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    - Wolfram|Alpha

    Seems right
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