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Thread: Laplace trnasform, Final in 4hours! please help!

  1. December 17th 2008, 12:46 AM #1
    AmyZheng
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    Laplace trnasform, Final in 4hours! please help!

    how do you derive the laplace transform for t^2 sin(3t)?
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  2. December 17th 2008, 12:52 AM #2
    Mush
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    \mathcal L (t^2 sin(3t)) = \int_0^{\infty} t^2sin(3t)e^{-st} dt

    I'm afraid it's a rather long and boring integration by parts.
    Last edited by Mush; December 17th 2008 at 01:13 AM.
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  3. December 17th 2008, 03:00 AM #3
    mr fantastic
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    Quote Originally Posted by AmyZheng View Post
    how do you derive the laplace transform for t^2 sin(3t)?
    Use the following operational theorem:

    LT[t^2 \, f(t)] = F''(s) where LT[f(t)] = F(s).

    In your case f(t) = \sin (3t) \Rightarrow F(s) = \frac{3}{s^2 + 3^2}.
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