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Homework Help: Laplace from first principles

  1. Nov 5, 2008 #1
    1. The problem statement, all variables and given/known data

    Find, from first principles, the Laplace transform of f(t) = sin2(3t)

    2. Relevant equations

    sin23t = 1/2(1-cost(6t))

    L{SINat} = a/(s2 + a2)

    3. The attempt at a solution

    I already have the solution.

    s/2(s2 + 36)

    What I want to ask is what does the first principles part mean? Is that asking me to integrate or look at the table of transforms? I don't quite understand what method I'm suppose to use for the transformation. Any light on this topic would be heavily appreciated.
    Last edited: Nov 5, 2008
  2. jcsd
  3. Nov 5, 2008 #2


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    Science Advisor

    The Laplace transform of a function, f(x) is defined as
    [tex]L(f)(s)= \int_0^\infty e^{-sx}f(x)dx[/tex]
    "From first principles" means using that formula. I recommend integrating by parts.
  4. Nov 5, 2008 #3
    I see. That makes sense.

    Thank you very much for your help.
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