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Finding ZIR given a diff eq

  1. Apr 16, 2007 #1
    1. The problem statement, all variables and given/known data
    Calculate ZIR(t) for the system described for the following differential equation, where the initial condition is y(0-) = 5:


    2. Relevant equations
    2y' + 3y = 2x' + x(t-1)


    3. The attempt at a solution
    I'm pretty sure we're supposed to laplace-transform it, then find Y/X = H(s) then inverse back to time domain.
    2*(s*Y - 5) + 4*Y = 2*(s*X) + X*exp(-s)
    cannot be solved for Y/X, which makes me think I somehow messeed up the initial transform, or perhaps the method altogether
     
    Last edited: Apr 16, 2007
  2. jcsd
  3. Apr 17, 2007 #2

    SGT

    User Avatar

    For the ZIR you must have no imput. So, you must solve
    2y´ + 3 y = 0 with y(0) = 5
    For the zero state response you solve
    2y´ + 3y = 2x´+ x(t-1)
    The complete response is the sum of the two.
     
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