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Homework Help: Steady state solution

  1. Sep 14, 2007 #1
    1. The problem statement, all variables and given/known data

    What is the steady state solution to the equation

    4y''+4y'+17y=202cos3t (*) ?

    2. The attempt at a solution

    The steady state solution is, if I've got it right, only the particular solution. It's got to be on the form

    Kcos3x+Msin3x.

    I calculate the derivatives, put into (*) and find it to be 122,19 cos 3t + 210 sin 3t.

    It's normal to write steady state solutions on the form

    Ccos(ωt-η).

    How can I do that?
     
  2. jcsd
  3. Sep 14, 2007 #2
    If I tell you that K cos(A+B) = K cos A cos B - K sin A sin B = C cos A + D sin A,

    could you find B and K if you were given C and D ?
     
  4. Sep 14, 2007 #3
    K=sqrt(C^2+D^2)

    tan B =D/C

    Found some formulas on the internet. Is it correct?
     
    Last edited: Sep 14, 2007
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