1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    sharks

    User Avatar
    Gold Member

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

    ehild

    User Avatar
    Homework Helper
    Gold Member

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


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

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    [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.
    WHICH WILL BE
    2cos(3t)/(D^2+D+1)
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook