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Inverse Laplace transform (Initial Value Problem)

  1. Sep 21, 2013 #1
    1. The problem statement, all variables and given/known data

    I'm stuck trying to find out the inverse Laplace of F(s) to get y(t) (the solution for the differential equation):

    Y(s) = 1 / [ (s-1)^2 + 1 ]^2



    3. The attempt at a solution

    I tried using a translation theorem and then apply the sine formula, but the denominator is still all squared. I also tried partial fractions to expand Y(s) but I didn't get it right...

    Any suggestions please?
     
  2. jcsd
  3. Sep 21, 2013 #2

    Ray Vickson

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    Yes: show us what you did and what you got. How can we possibly help if we have no idea of what your problem is?
     
  4. Sep 21, 2013 #3
    [itex][(s-1)+1]^2=[(s-1+i)(s-1-i)]^2[/itex]

    Therefore, [tex]\left[\frac{1}{ (s-1-i)(s-1+i) }\right]^2=\left[\frac{1}{2i}\left(\frac{1}{s-1-i}-\frac{1}{s-1+i} \right ) \right ]^2[/tex]

    Can you continue it from there?
     
  5. Sep 22, 2013 #4

    My friend, that's the thing, I can't get past that. I stated the problem clearly: "I'm stuck trying to find out the INVERSE LAPLACE of the given Y(s) to get y(t)". There's no point in showing what I did before, it's not needed for what's after the equation I posted.

    Anyway, I got it. It was just applying one of the formulas from the Laplace transform tables. I thought partial fractions or something else had to be done.

    Thanks for your help
     
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