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Homework Help: Laplace transform of sin(2t)cos(2t)

  1. Mar 18, 2009 #1


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

    Find the Laplace transform of

    f(t) = sin(2t)cos(2t)

    using a trig identity.

    2. Relevant equations


    3. The attempt at a solution

    I know the double-angle formula sin(2t) = 2sin(t)cos(t) but that's not helping much. Can you give me some advice on how to proceed.
  2. jcsd
  3. Mar 18, 2009 #2
    Consider that

  4. Mar 19, 2009 #3


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    Okay, then [tex]\sin{(2t)}\cos{(2t)} = 1/2\sin{(t)}\cos{(t)}[/tex]

    The Laplace integral is then:


    So where do I go from here to solve this? The [tex]e^{-st}[/tex] is throwing me off, otherwise I'd just do a u substitution with [tex]u = \sin{(t)}[/tex] and [tex]du = \cos{(t)}dt[/tex].
  5. Mar 19, 2009 #4
    Well if you have that




    So then if you want to do it from the integral you just need to integrate


    where the [itex]s[/itex] you treat as a constant (you're integrating with respect to [itex]t[/itex]). But you could just use the known laplace transform for [itex]\sin{(at)}[/itex] unless you are meaning to derive it.
  6. Mar 19, 2009 #5


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    Ahhhh lights coming on. Thanks for the help!
  7. Mar 19, 2009 #6
    Ah good--glad to help.
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