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

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

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

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

    Good luck.
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  3. #3
    Member zangestu888's Avatar
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    can i use the first shifting therom for $\displaystyle

    \mathcal{L}\left\{e^{-t} \cos{3t}\right\}
    $
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    Quote Originally Posted by pomp View Post
    to work out $\displaystyle \mathcal{L}\left\{e^{-t} \cos{3t}\right\}$

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

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

    Seems right
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