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Laplace question

  1. May 13, 2007 #1
    I want to find the following inverse Laplace transform:


    I was thinking of using the second shift theorem to no avail.

    I have tried the question and my answer is :

    This does not seem to be a plausible answer since I modified the second
    shift theorem.

    {If only the question was to inverse [5/(s+2)]exp(-2s),
    then my answer would have been 5(exp-2t)u(t-2) (which hopefully is right).
    However the question is different.}
  2. jcsd
  3. Jul 21, 2007 #2
    I just want to make sure I understand the equation. Is it:

    [tex]\frac{5e^{-2s}}{s+1}[/tex] ?

    If it is, I think this is simpler than you're making it.

    [tex]\frac{5e^{-2s}}{s+1} = \frac{K}{s+1}[/tex]

    Multiply both sides by [tex]s+1[/tex] and evaluate at [tex]s = -1[/tex]:

    [tex]5e^{-2(-1)} = K[/tex]

    [tex]5e^{2} = K[/tex]

    Now plug it back in:


    Now the inverse laplace would be:

    [tex]L^{-1} = 5e^{2}e^{-t} u(t)[/tex]


    [tex]L^{-1} = 5e^{2-t} u(t)[/tex]

    I hope this helped.
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