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Laplace Transform

  1. Nov 6, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the Laplace Transform of the following:

    [tex]5{\delta (t-3)}+4{u(t-2)}+3{e^{-5(t-3)}u(t-4)}[/tex]


    3. The attempt at a solution
    I know how to do the first and second terms, but I'm having trouble with the third.

    [tex]5e^{-3t}+4\frac{1}{s}e^{-2t} + ?[/tex]

    I think I should be using either

    [tex]L\{ f(t-t_0)u(t-t_0) \} = e^{-st_0}F(s)[/tex]

    or

    [tex]L\{ e^{-\alpha t}u(t) \} = \frac{1}{s+\alpha}[/tex]

    or both.

    The problem is, in the first one, I don't know what to put for [tex]F(s)[/tex].

    Any help would be appreciated.
     
    Last edited: Nov 6, 2007
  2. jcsd
  3. Nov 6, 2007 #2
    Unfortunately, you can't use your first equation because [tex]t_0[/tex] in f and u are not the same.

    Try breaking up the exponential using algebra first.
     
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