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Homework Help: Understand Laplace alot better now

  1. Sep 17, 2005 #1
    Ok, I'm starting to understand Laplace alot better now. But I have, hopefully, my last question. If you have a function like

    g(t)=t^2 * sin(3t) * x(t) where x(t) has an already defined laplace transform.

    do you actually include x(t) in your laplace transformation? Because when I see other problems that have u(t) at the end you don't really do anything with them, you only worry about the terms in front of it. Like f(t)=sin(3t)u(t), the answer is simply 3 / (s^2 + 9)....u(t) is not included in it.
     
  2. jcsd
  3. Sep 17, 2005 #2

    Tom Mattson

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    Yes, you do.

    That's because u(t)=1 over the entire range of integration in the transform. If you had instead u(t-a), a>0, then you could not just drop it.
     
  4. Sep 17, 2005 #3

    So for the problem:
    g(t)=t^2 * sin(3t) * x(t)

    How would you go about transforming that? This is my first encounter of 3 terms...
     
  5. Sep 18, 2005 #4

    GCT

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    yeah, you'll probably need to review the chapter the step functions/laplace.

    By the way, ever heard of convolution integrals?
     
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