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Inverse Laplace transform for 1/(350+s) * X(s)

  1. Nov 24, 2016 #1
    Hi, everyone, the question is as below:

    Find the inverse Laplace transform to 1/(350+s) * X(s). 's' is the Laplace variable and 'X(s)' is also a variable.

    I inverted 1/(350+s) and X(s) separately and multiplied them together directly. But this seems not giving me the correct answer. Could anyone help me on this?

    Thank you.
    Last edited by a moderator: Nov 24, 2016
  2. jcsd
  3. Nov 24, 2016 #2

    Ray Vickson

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    Multiplication won't work; you need convolution.

    If ##f(t) \leftrightarrow F(s)## and ##g(t) \leftrightarrow G(s)##, then ##F(s) G(s)## is the Laplace transform of the convolution ##f*g##, where
    $$(f * g)(x) = \int_0^{\infty} f(y) g(x-y) \, dy = \int_0^{\infty} f(x-y) g(y) \, dy .$$
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