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Laplace transform

  1. Dec 1, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the Laplace transform of L{texp(9t)sin(2t)}

    2. Relevant equations
    (-1)^n F^n (s)


    3. The attempt at a solution
    I am not sure how to start it. The exp(9t) term throws me off. Usually I would just do (-1) F'(s) where F(s) is the laplace of sin(2t). But do I take the derivative of exp(9t) in addition to sin(2t)? Multiply them together?
    Thanks in advance!
     
  2. jcsd
  3. Dec 2, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You can start by using the definition of Laplace transform:
    [tex]\int_0^\infty f(t)e^{-st}dt[/tex]

    Here, [itex]f(t)= t e^{9t} sin(2t)[/itex] so that integral is
    [tex]\int_0^t te^{(9- s)t} sin(2t) dt[/tex]

    Integration by parts should do that. The obvious choice is u= t, [itex]dv= e^{(9-s)t}sin(2t)dt[/itex] and you will have to do another integration by parts to find v.
     
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