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Step function - laplace

  1. Mar 16, 2009 #1
    step function - laplace....

    1. The problem statement, all variables and given/known data
    y"+y = f(t)

    f(t) = 1, t<pi/2
    0, pi/2<=t<infinity

    3. The attempt at a solution

    i now have L{y} = [tex]\frac{1-e^(-(pi/2)s)+s}{s(s^2+1)}[/tex]

    but how do i separate them and finish the problem?

    thanks
     
  2. jcsd
  3. Mar 16, 2009 #2

    HallsofIvy

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    Staff Emeritus
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    Re: step function - laplace....

    Use partial fractions like always.
    [tex]\frac{1}{s(s^2+ 1)}= \frac{A}{s}+ \frac{Bs+ C}{s^2+ 1}[/tex]

    Find A, B, and C.
     
  4. Mar 16, 2009 #3
    Re: step function - laplace....

    so no i have f(t) = 1-cos(t)+sin(t) - L{[tex]\frac{e^(pi*t/2)}{s(s^2+1)}[/tex]}

    how do i get the last laplace?
     
    Last edited: Mar 16, 2009
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