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Inverse Laplace transform

  1. Oct 16, 2009 #1
    1. The problem statement, all variables and given/known data
    hi guys, i need to find the inverse Laplace transform of

    s/((s+1)^(2) +4)

    the acual question is an IVP, i have worked trough it and am just about finished but i am stuck on this transform.

    how would you go about getting this into a form that can be transformed like
    2/((s+1)^(2) + 4)

    or is it already and i am missing something

    2. Relevant equations

    i guess it can be changed to

    s/(s^2 + 2s + 5) but that seems worse




    3. The attempt at a solution




    thanks for any help
    i hope this is the right spot for this post
     
  2. jcsd
  3. Oct 16, 2009 #2

    lanedance

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    Homework Helper

  4. Oct 16, 2009 #3
    thanks lanedance

    i dont believe that i am expected to derive it myself as im sure i read somewhere that i wasnt expected to for this course.

    i have looked through a few simular tables without much luck im afraid.



    it may be possible that i messed up further up the question and have arived at a step i dont need to do, ill go back through and check things. hopefully i get lucky
     
  5. Oct 17, 2009 #4

    lanedance

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    the form in the table matches your function though
     
  6. Oct 17, 2009 #5
    you mean 1/s^n, example 2.7a

    i dont really see how that matches
    s/((s+1)^(2) +4)

    would it be possible for you to explain
     
  7. Oct 17, 2009 #6

    lanedance

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    have a look at entry 2.27a as mentioned
    [tex] \frac{s+\lambda}{(s+\alpha)^2 + \beta^2} \rightarrow e^{- \alpha t}(cos(\beta) \frac{\lambda - \alpha}{\beta}sin(\beta t))[/tex]
     
    Last edited: Oct 18, 2009
  8. Oct 18, 2009 #7
    oh, cool, thanks.

    missed that completly.


    thanks again
     
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