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Multiplication in a LaPlace Transform

  1. May 25, 2010 #1

    TG3

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    The problem statement, all variables and given/known data
    Find the Laplace transform of the given function, a and b are real constants.
    Hint: cos(bt)=(e^ibt+e^-ibt)/2 and sin(bt)=(e^it-e^ibt)/2i.

    f(t)=e^(at)*sin(bt)

    The attempt at a solution

    The LaPlace transform of e^at is 1/(s-a).

    The LaPlace transform of sin(bt) is b/(s^2+b^2).

    Simply multiply those together, I got b/s^3-as^2+bs^2-ab^2.

    This is wrong, and it feel like I'm making a very basic mistake that should be obvious, doing something other than multiplying the two seperate LaPlace transforms together. So, what am I supposed to do when the function I am supposed to work with has two easily distinguishable functions within it?
     
  2. jcsd
  3. May 25, 2010 #2

    LCKurtz

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    Have you had the shifting theorems? Like for L(eatf(t)) in terms of L(f(t))?
     
  4. May 25, 2010 #3

    TG3

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    I don't think so, but I'm not positive... I have trouble focusing for the entire period.
     
  5. May 25, 2010 #4

    LCKurtz

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    Well, if you haven't had the shifting theorem, you can always use the given hint. Express the sine in terms of exponentials, take the transform, and simplify it.
     
  6. May 25, 2010 #5

    vela

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    Start by plugging that function into the definition of the Laplace transform and combining the exponentials. You might be able to see the answer immediately.
     
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