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Math Help - Laplace Transformation Question.

  1. #1
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    Laplace Transformation Question.

    Not sure how to start this question -.-

    Find the Laplace transform of the function:

    f(t)=te^(2t)cos(2t)

    f(t)= ?

    Thanks for the help!!
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  2. #2
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    Hi there, been a while since i've done one of these, the definition is

     \mathcal{L}\left\{f(t)\right\}=\int_0^\infty e^{-st}f(t)~dt<br />

    Therefore

     \mathcal{L}\left\{te^{2t}cos(2t)<br />
\right\}=\int_0^\infty e^{-st}te^{2t}\cos(2t)~dt=\int_0^\infty e^{t(2-s)}t\cos(2t)~dt<br />

    Also by the shift theorem

    \mathcal{L}\left\{e^{2t}\cos(2t)\right\}=\frac{s-2}{(s-2)^2+4}
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  3. #3
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    Ohhh I see now

    I can use the the Theorem of Differentiation of transforms after that shift transformation.

    Ima give it a try now!!
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  4. #4
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    Thanks for the help!! I got the correct answer!!

    It's

    (s*(s-4))/((s^2-4s+8)^2)
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  5. #5
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    Do you mean?

     \mathcal{L}\left\{t\times f(t)\right\}=-F'(s)<br />
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  6. #6
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    Quote Originally Posted by Phyxius117 View Post
    I got the correct answer!!
    Nice one!
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  7. #7
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    yes that's the one!!
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