Laplace Transform

  • Thread starter EugP
  • Start date
  • #1
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Homework Statement


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]


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:

Answers and Replies

  • #2
42
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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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