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Laplace transform of convolution with derivative in it

  1. Oct 9, 2011 #1
    1. The problem statement, all variables and given/known data

    Hi,

    I am wondering how to Laplace transform this expression

    [tex]f(t)=\int^{\tau}_{0} g(\tau)f'(t-\tau)d\tau[/tex]
    or more precisely
    [tex]f(t)=\int^{\tau}_{0} sin(8\tau)f'(t-\tau)d\tau[/tex]

    The [tex]f'(t-\tau)[/tex] gets me confused.

    2. Relevant equations

    [tex]\int^{\tau}_{0} f(t-\tau)g(\tau)d\tau[/tex]
    and the laplace transform of that is:
    [tex]F(s)G(s)[/tex]

    3. The attempt at a solution
    I have no idea how to proceed.

    Maybe
    [tex]F(s)=8/(s^2+8^2)(sF(s)-f(0))[/tex]
     
    Last edited: Oct 9, 2011
  2. jcsd
  3. Oct 9, 2011 #2
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