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Laplace transformations

  1. Oct 15, 2008 #1
    I'm trying to transform some functions. These two I haven't succeeded transforming:

    f(t) = cos((omega)t + tetha)

    f(t) = sint*cost

    Also, I need help to find the inverse transform of this function:

    F(s) = 8 / (s^2 + 4s)
  2. jcsd
  3. Oct 15, 2008 #2


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    Show us what you tried. It looks to me like you can just take the definition of the laplace transform and integrate by parts twice for the first one.
  4. Oct 15, 2008 #3
    Hey Dick, I have the same question, laplace of cos(t). I did the integration by parts twice and got to the point where I need to take the limit. Now thats where I'm stuck. There is no limit of cosine and sine. They diverge to infinity. Rather they are bounded between 1 and -1. So what do I do?

    Here is my solution.


    Too large to paste as an image. Its long but very very clearly defined what I did.

    Thanks for the help in advance.

    Edit: You can go ahead and write on my image to show mistakes. I noticed that I forgot about the 1/s when subtracting the integral from both sides. That should make a difference, but it still doesnt help with the limit as b goes to infinity.

    I know I made mistakes, what are they exactly though.
    Last edited: Oct 15, 2008
  5. Oct 15, 2008 #4


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    The limits are not a problem sin(t) and cos(t) may oscillate but lim e^(-st) -> 0 at infinity. So evaluated between 0 and infinity sin(t)e^(-st) gives 0 and cos(t)e^(-st) gives -1. And the laplace transform of cos(t) is s/(1+s^2). That's what you are looking for. If A=laplace transform of cos(t), then the integration by parts should lead you to the conclusion A=1/s-A/s^2. Now solve for A.
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