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Laplase question

  1. Jul 22, 2009 #1
    [tex]
    f(t-a)u_a(t)->F(s)e^{-as}
    [/tex]
    [tex]
    g(t)={\cos (t),0<=t<\pi}
    [/tex]
    [tex]
    g(t)={0,t>=\pi}
    [/tex]

    [tex]
    g(t)=\cos(t)[ u(t)-u(t-\pi)]=\cos(t) u(t)-\cos(t) u(t-\pi)=\frac{s}{s^2-1}+??\\
    [/tex]

    i cant apply the formula in the last part
     
  2. jcsd
  3. Jul 22, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Trig formula [itex]cos(t-\pi)= -cos(t)[/itex].
     
  4. Jul 22, 2009 #3
    [tex]g(t)=\cos(t)[ u(t)-u(t-\pi)]=\cos(t) u(t)+\cos(t-\pi) u(t-\pi)=\frac{s}{s^2-1}+\frac{s}{s^2-1}e^{-\pi}\\[/tex]

    is it correct?
     
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