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Homework Help: Stedy State of damped system

  1. May 1, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the steady-state solution having the form https://webwork3.math.ucsb.edu/webwork2_files/tmp/equations/e1/348e8eb8a4ddf62dd06b46276196e71.png [Broken] for the damped system x'' + x' + x = 2cos(3t)

    2. Relevant equations

    Acos3t + bsin3t

    3. The attempt at a solution

    To be honest, I wasn't sure how to do this problem, so I just tried undetermined coefficients and got (-16/73)cos(3t)+ (6/73)sin(3t), which was wrong :< muuu
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. May 1, 2012 #2


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    Why is (-16/73)cos(3t)+ (6/73)sin(3t) less than the variable "muuu"? :surprised
  4. May 1, 2012 #3


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    It is the correct steady-state solution, but you need to convert it to the given form xss=Ccos(3t-δ).

    Last edited by a moderator: May 6, 2017
  5. May 1, 2012 #4


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    [tex]Acos(\omega t- \delta)= Acos(\delta)cos(\omega t)- Asin(\delta)sin(\omega t)[/tex]
    With [itex]\omega= 3[/itex]. What are A and [itex]\delta[/itex]?
  6. May 1, 2012 #5
    yo need to calculate the particular integral of it.
    where D is what I think you can guess.multiply and divide by D^2-D+1 on left.the denominator will contain only even powers of D.put D^2=-9 in denominator and carry out the differentiation in numerator after that to find the result and if you don't get it see any book on differential eqn to find out the P.I. of it.C.F.will not contribute because it will be zero in steady state.
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