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Math Help - inverse Laplace transform

  1. #1
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    inverse Laplace transform

    Hi all,

    Using the s shifting theorem to find the inverse Laplace transform of:

    F (s) = 3 / (s + 2)^2

    I get the right answer but i am not sure if my working out is correct, would be appreciated if someone can tell me.

    F(s +2) = L [e^(2t)* f(t)]

    L[f(t)] = 3/ s^2

    f(t) = L^(-1) [3/ s^2]
    = 3t

    g(t) = e^(2t) * f(t)
    g(t) = 3t*e^(2t)

    Thanks in advance,
    ArTiCk
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  2. #2
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    Quote Originally Posted by ArTiCK View Post
    Hi all,

    Using the s shifting theorem to find the inverse Laplace transform of:

    F (s) = 3 / (s + 2)^2

    I get the right answer but i am not sure if my working out is correct, would be appreciated if someone can tell me.

    F(s +2) = L [e^(2t)* f(t)]

    L[f(t)] = 3/ s^2

    f(t) = L^(-1) [3/ s^2]
    = 3t

    g(t) = e^(2t) * f(t) Mr F says: This should be {\color{red}e^{-2t} \cdot f(t)} . Note that F(s + 2) = F(s - [-2]) ....

    g(t) = 3t*e^(2t) Mr F says: This should be {\color{red}3t \cdot e^{-2t}}

    Thanks in advance,
    ArTiCk
    By the way, * is not a good symbol to use for multiplication when posting laplace transform problems - it could get confused with the convolution operator.
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