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Homework Help: Step functions

  1. Nov 29, 2005 #1
    i have f(t) defined piece-wise and continous..
    f(t) = 0, t < 2pi
    t-pi , pi <=t<2pi
    0 , t >=2pi

    i have so far g(t)=U_pi*f(t-pi)-U_2pi*f(t-pi)
    if i do the laplace,
    i get e^-pis/s^2-e^-2pis/s^2
    in the book, they have
    e^-pi*s/s^2 -e^-2pi*s/s^2 (1+pi*s)
    I am not sure how they got the factor of (1+pi*s)
  2. jcsd
  3. Nov 30, 2005 #2
    Are you sure [itex] f(t) [/itex] is correct. You have:
    [tex] f(t) = \left\{ \begin{array}{l} 0, \,\, t<2\pi \\ t-\pi, \,\, \pi \leq t < 2\pi \\ 0, \,\, t \geq 2\pi [/tex]

    So when [itex] t<2\pi [/itex] and [itex] \pi \leq t < 2\pi \\ [/itex] it equals [itex] 0 [/itex] and [itex] t-\pi [/itex]. I'm assuming you mean [itex] f(t) = 0|t<\pi [/itex] ?

    I got (assuming [itex] f(t) [/itex] is wrong):

    [tex] \frac{e^{-\pi s}}{s^2} - \frac{\pi e^{-2\pi s}}{s} - \frac{e^{-2\pi s}}{s^2} [/tex]
    Last edited: Nov 30, 2005
  4. Nov 30, 2005 #3
    sorry, what i meant was
    on the first interval, t < pi, not two pi.
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