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Inverse Laplace Transfroms

  1. Nov 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Hello,

    I have just started studying Laplace transformations and I am struggling to identify reverse Laplace transforms. I understand how to perform the transform, but going the other way is really confusing me.

    i.e, given ##F(P)## find ##f(t)##.

    If I have that ##F(P) = \frac{5 - 2P}{P^{2} + P - 2}##, and have been told to use the facts that;

    ##\frac{e^{-at} - e^{-bt}}{b - a} = \frac{1}{(P+a)(P + b)}## and

    ##\frac{ae^{-at} - be^{-bt}}{a - b} = \frac{P}{(P+a)(P + b)}##

    to find f(t)



    2. Relevant equations


    3. The attempt at a solution

    I think a good first step is to recognise that the denominator can be factorised;

    ##F(P) = \frac{5 - 2P}{(P - 1)(P + 2)}##

    but I am very confused about what I need to be looking for to move forward. I would really appreciate some guidance here.

    Thank you
     
  2. jcsd
  3. Nov 9, 2015 #2

    Orodruin

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    Split it in two terms, one with the numerator proportional to P and one constant, and just identify with the terms in the hint you got.
     
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