Inverse Laplace

Discussion in 'Homework Help' started by Hasnatsaeed, Dec 11, 2010.

  1. Hasnatsaeed

    Thread Starter New Member

    Sep 23, 2010
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    Hi..i need to determine the inverse laplace of F(s)=((s^2)-(∏^2))/((s^2)+(∏^2))^2..........by either differentiation or integration of Transforms method..no other methods..i know thee inverse laplace of this s-domain function is t cos(∏t) but i cant figure out a way to show this through either of the two methods mentioned.plz help thanks
     
  2. tyblu

    Active Member

    Nov 29, 2010
    199
    16
    This belongs in the math forum.

    <br />
F(s) = \left(\frac{s^2-\pi^2}{s^2+\pi^2}\right)^2 \\<br />
\\<br />
\text{Let } Y(s) = \frac{s^2-\pi^2}{s^2+\pi^2} <br />
 = \frac{s^2}{s^2+\pi^2} - \frac{pi^2}{s^2+\pi^2} \\<br />
\\<br />
\mathscr{L}^{-1}\{Y(s)\}<br />
 = \mathscr{L}^{-1}\{\frac{s^2}{s^2+\pi^2} - \frac{pi^2}{s^2+\pi^2}\}<br />
 = \mathscr{L}^{-1}\{\frac{s^2}{s^2+\pi^2}\} - \mathscr{L}^{-1}\{\frac{pi^2}{s^2+\pi^2}\}<br />

    You do the next part, and indicate where you get stuck.
     
  3. Hasnatsaeed

    Thread Starter New Member

    Sep 23, 2010
    27
    0
    its F(s)=((s^2)-(∏^2)) / ((s^2)+(∏^2))^2....the denominator is squared not the whole expression and i am supposed to determine the inverse laplace through either differentiation or integration of laplace.i.e by either using......L{tf(t)}= -F'(s)...or......L{f(t)/t}=∫F(s).ds(the limit is from 0 to ∞)
     
  4. Hasnatsaeed

    Thread Starter New Member

    Sep 23, 2010
    27
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    i tried to put it into the math section but due to double threads it was closed:(..so i cant actually
     
  5. bertus

    Administrator

    Apr 5, 2008
    19,507
    3,972
    Hello,

    I said, you can continue here.
    This thread was already on the go.

    Bertus
     
  6. tyblu

    Active Member

    Nov 29, 2010
    199
    16
  7. Hasnatsaeed

    Thread Starter New Member

    Sep 23, 2010
    27
    0
    To use any one of the methods mentioned i have to either first differentiate it or integrate it with respect to s and then take their inverse laplace and then multiply or divide by t depending upon whether i am following differentiation method or integration..thats the approach i am supposed to follow. you are just telling me to get the answer out straight foreward by taking inverse laplace.
     
  8. Hasnatsaeed

    Thread Starter New Member

    Sep 23, 2010
    27
    0
    if i differentiate i get this.now the inverse laplace of this is equal to -tf(t)...now how can i show that f(t)=tcos(pi.t)?
     
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