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Math Help - Inverse of Laplace Transform

  1. #1
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    Inverse of Laplace Transform

    Iam trying to find the inverse of the attached laplace transform,
    Dont know how to rearrange the 1st part to get it into a standard form to apply the inverse?

    I've tried using partial Fraction but I have the exponential term I dont know what to do with?
    The correct ans is on the bottom of the page.
    Attached Thumbnails Attached Thumbnails Inverse of Laplace Transform-laplace.pdf  
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  2. #2
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    Hint: \displaystyle \mathcal{L}^{-1}\left[e^{-as}F(s)\right] = f(t-a)H(t-a).
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    thanks prove it ,i'll give it another go
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    I can see that e^(-2t) = H(t-2)



    but cant see how to get F(s) out of 1/(s^3 + s)



    L{f(t)} = F(s)
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    Quote Originally Posted by heatly View Post
    but cant see how to get F(s) out of 1/(s^3 + s)
    Hint: What is the Laplace transform of 1 - cos(kt)?

    -Dan
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  6. #6
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    Quote Originally Posted by heatly View Post
    I can see that e^(-2t) = H(t-2)



    but cant see how to get F(s) out of 1/(s^3 + s)



    L{f(t)} = F(s)
    Factorise the denominator and use Partial Fractions.
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  7. #7
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    Thanks a heap prove it and topsquark.

    I finally got it.
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