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Math Help - Laplace Transform

  1. #1
    Member roshanhero's Avatar
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    Laplace Transform

    What is the Laplace Transform of f(x)=e^{bx}.sin ax
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by roshanhero View Post
    What is the Laplace Transform of f(x)=e^{bx}.sin ax
    put it in formula for Laplace transformation and try to solve

    Bilateral Laplace transformation :

    \displaystyle F(S)= \int _{-\infty} ^{+\infty} e^{-st}f_{(t)} \;dt
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  3. #3
    Member roshanhero's Avatar
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    I am trying but the things are getting messy though..........
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  4. #4
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by roshanhero View Post
    I am trying but the things are getting messy though..........
    hmmmm.... as I recall from signal and systems, Laplace transformation doesn't exist on periodical signals like u have there ...
    there is Laplace transformation of  \displaystyle sin (\omega_0 t) u(t) because with step function  u(t) u put to zero your signal for all t<0, But with like this one u have (periodical) it doesn't converge


    P.S. perhaps only if u use unilateral Laplace transformation (but still I'm spinning a lot even that way) which limits go from (-0) to infinity... but as I said i think there's no point going there because it just start going in circles (at least I do)



    Edit : without your "constants" (a) and (b) and using unilateral formula (don't know if you are bounded to use bilateral) u get this :
     \displaystyle \frac {1}{S^2-2S+2} that's for  ROC : Re(S) >1 (region of convergence )

    without (a), or should i say a=1 u'll get :

     \displaystyle \frac {1}{(b-S)^2+1} that's for  ROC :Re(b)< Re(S)
    Last edited by yeKciM; August 8th 2010 at 11:20 AM.
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  5. #5
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    Quote Originally Posted by roshanhero View Post
    What is the Laplace Transform of f(x)=e^{bx}.sin ax
    There is a standard operational formula that will handle this. I suggest you go to your table of Laplace transforms and find it. Then use it. If you have any further difficulties, please post your work and say where yuo are stuck.
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  6. #6
    Senior Member yeKciM's Avatar
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    yes, always u can use table of Laplace transformations, but on the exams i don't think anywhere would someone allow you to use table of Laplace transformations... or that's just me
    anyway using unilateral u can get to the solution, but using bilateral u can't

    solution should be something like:

    \displaystyle \frac {a}{(S-b)^2+a^2} with ROC: Re(S)>Re(a)
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