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Differential Equation (Laplace transform involving a convolution)

  1. Nov 26, 2015 #1
    So I have to solve an initial value problem involving the Laplace Transformation method. I have all the terms in Y(t) besides one term, I cannot figure how to change it from frequency domain back into time domain.


    Not sure how to type in Latex, so i uploaded a picture, using the whiteboard feature on this webpage.

    When I try to use the definition of the convolution, where F*G, I'm not sure what to do with unit function and
    cos(4t-4pie), in other words how to change them into tao.
     

    Attached Files:

  2. jcsd
  3. Nov 27, 2015 #2
    unit piecewise defined function, not unit function.
     
  4. Nov 27, 2015 #3

    vela

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    You should spend a few minutes and learn how to use LaTeX.

    You have ##Y(s) = e^{-\pi s} \frac{s}{(s^2+16)^2}##. If you want to split it up and use convolution, I'd rewrite it as
    $$Y(s) = \frac 14 e^{-\pi s} \left(\frac{s}{s^2+16}\right)\left(\frac{4}{s^2+16}\right).$$ You can deal with the delay at the end. So now you have ##f(t) = \cos 4t## and ##g(t) = \sin 4t##. What's the definition of convolution?
     
  5. Nov 27, 2015 #4
    Is there an easy guide to learning latex?

    So I can post the response and make it easier for you guys.
     
  6. Nov 27, 2015 #5

    vela

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  7. Nov 27, 2015 #6

    NascentOxygen

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    If you click on "Reply" you'll be able to see the Latex instructions that others have used to produce their post.
     
  8. Nov 27, 2015 #7
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