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

    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
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    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
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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
    15,649
    2,348
    Hello,

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

    Bertus
     
  6. tyblu

    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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