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Easy Laplace Transform help!

  1. Dec 17, 2009 #1
    "easy" Laplace Transform...help!

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

    Evaluate L{(e^-2t)*t*sinht}

    2. Relevant equations

    translation theorem

    3. The attempt at a solution

    Just to clarify: the contents of the bracket is the product of 3 terms:
    e^-2t (e to the power of -2t)

    all multiplied together.

    I am ok with finding the laplace of 2 term products but with 3 terms I do not know where to begin. All I can think of is that the presence of the euler term suggests the use of the 2nd translation theorem.

    Any help would be appreciated.
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Dec 17, 2009 #2


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    Homework Helper

    Re: "easy" Laplace Transform...help!

    Start with L{sinhkt}, I hope you know what this is.

    Now use the fact that L(tf(t)}= -F'(s)

    Now just apply the shift property for L{e-2tf(t)}
  4. Dec 17, 2009 #3
    Re: "easy" Laplace Transform...help!

    You can express sinh t in terms of e^t and e^-t. Do that and combine all the exponentials together. That way you can express the whole thing as a sum of Laplace transforms of t at different points.
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