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Phasors and steady-state solutions

  1. Oct 27, 2008 #1
    1. The problem statement, all variables and given/known data
    use phasors to evaluate the steady-state solution to the equation f'' + 1.5f' + f = Ce^2tj


    2. Relevant equations



    3. The attempt at a solution
    let f = Ce^2tj (this is a 'trial solution', i think)

    f' = 2tCe^2tj
    f'' = 4(t^2)Ce^2tj

    therefore 4(t^2)Ce^2tj + 3tCe^2jt + Ce^2tj = Ce^2tj
    4t^2 + 3t = 0

    therefore t = 0 and t = -3/4
    therefore f = C and f = Ce^-1.5tj.

    ^ the above is NOTHING like the answer. what am i doing wrong?
     
  2. jcsd
  3. Oct 27, 2008 #2
    attempt #2:

    f = Ae^2tj
    f' = 2tAe^2tj
    f'' = 4(t^2)Ae^2tj

    so...

    4(t^2)Ae^2tj + 3Ate^2tf + Ae^2tj = Ce^2tj

    dividing through by e^2tj gives

    A(4t^2 + 3t + 1) = C

    so A = C/(4t^2 + 3t + 1)? that's still not the answer
     
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