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Inverse Laplace Transform

  1. Nov 19, 2011 #1
    1. The problem statement, all variables and given/known data
    the questions asks to determine inverse laplace transform of


    2. Relevant equations

    3. The attempt at a solution
    this can supposedly be done just using laplace transform tables so im guessing i need to simplify that to something thats workable but i dont know how.
    the solution is
    e^(-4t) (t^2/2 - (2/3) t^3)
    anyone can help in directing me how to simplify that equation before i use tables to inverse?
  2. jcsd
  3. Nov 19, 2011 #2

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    Welcome to PF, kiwifruit! :smile:

    Which transforms can you find that are somewhat close to your question?
    Or transforms that perhaps may be of help?
  4. Nov 19, 2011 #3
    i would say
    laplace of e^at = 1/(s-a)
    laplace of cos(at) = s/(s^2 + a^2)
    is similar to the question but i dont see how to simplify or factorize it to something workable
  5. Nov 19, 2011 #4

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  6. Nov 19, 2011 #5


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    I find this formula frequently helpful:

    [tex]\mathcal L^{-1}f(s+a) = e^{-at}\mathcal L^{-1}f(s)[/tex]

    If you rewrite the expression like this:
    and break it apart, the answer should fall right out.
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