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Laplace Transformation help~

  1. Apr 29, 2004 #1
    plz help me with this question

    Find the laplace transformation of this function

    i(t)=(t)(e^t)(sinkt)

    i really dont know how to do!
     
  2. jcsd
  3. Apr 29, 2004 #2
    The Laplace Transform is defined as:

    [tex]Y(s) = \int_{0}^{\infty} e^{-st}y(t)dt[/tex]

    where y(t) is the function you wish to find the Laplacian of.

    In this example, the integral would be:

    [tex]\int_{0}^{\infty} te^{-st}e^tsin(kt)dt[/tex]

    ...which is unbelievably ugly.

    Have you learned about convolution yet? This is a pretty nasty problem, unless I'm missing something, which it seems probable that I am.
     
    Last edited: Apr 29, 2004
  4. Apr 29, 2004 #3
    thz

    You didnt miss anything, i can do up to this stage, but it contain 3 t in it, I dont really know how to solve it!
     
  5. Apr 29, 2004 #4

    arildno

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    1. Since the integral of the e^((1-s)t)*sin(kt) will "rotate" during integration by parts (i.e. you will gain back a multiple of what you began integrating), evaluating the integral of this function alone should pose no problems.
    (Assuming s>1, that is)

    2. You can now go back to the original problem, using integration by parts to eliminate the t-factor.

    3. Alternatively, you might use the complex exponential as a simplifying measure.
     
  6. Apr 29, 2004 #5

    Tom Mattson

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    That's what I would do, too. The beautiful thing about that is that, not only is it a lot easier to calculate, but it also gives you TWO Laplace transforms simultaneously.

    mak_wilson, I would recommend that you take this suggestion. Make the replacement:

    sin(kt)--->eikt

    and take the imaginary part at the end.
     
  7. Apr 29, 2004 #6
    solution

    Here is a solution,
    Max.
     

    Attached Files:

  8. Apr 30, 2004 #7
    thank You~~
     
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