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Inverse Laplace transform

  1. Jul 21, 2014 #1

    kyu

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    1. The problem statement, all variables and given/known data

    Ds + E / (s^2 +1)^2

    2. Relevant equations



    3. The attempt at a solution

    Ds / (s^2 +1) + E / (s^2 +1)

    D[s/(s^2 + 1)^2] + E [1 / (s^2 + 1)^2]
     
    Last edited: Jul 21, 2014
  2. jcsd
  3. Jul 21, 2014 #2

    HallsofIvy

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    You mean, I assume (Ds+ E)/(s^2+ 1)^2

    That can be written as Ds/(s^2+ 1)^2+ E/(s^2+ 1)^2 but you seem to have lost the square on the denominator.
     
  4. Jul 21, 2014 #3

    kyu

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    i added it.. then what should i do next? no idea how to find the inverse
     
  5. Jul 21, 2014 #4

    vela

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    Consult a table of Laplace transforms.
     
  6. Jul 21, 2014 #5

    Ray Vickson

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    The standard way is to "know" a number of Laplace transforms already, plus some rules like the connection between the transforms of ##f(t)## and those of ##f'(t)##, ##\int_0^t f(\tau) \, d\tau## or ##f(t-a)## for constant ##a##--and similar general facts. Then you just try to "recognize" your ##\hat{f}(s)## among those mentioned above, and so know it inverse right away.

    There are also general "inversion" formulas, but they are hardly ever used in applications to get inverses.

    I suggest you struggle with this problem; it will teach you a lot, and you will be stronger for it after you are finished.
     
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