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Coupled Oscillators

  1. Nov 12, 2014 #1
    1. The problem statement, all variables and given/known data
    1. Note this question is from Morin 4.35. The system in the example in Section 4.5 is modified by subjecting the
      left mass to a driving force Fd*cos(2ωt), and the right mass to a driving
      force 2Fd cos(2ωt), where ω^2 = k/m. Find the particular solution for x1 and x2.

      Just to note the equations of motion of the example in section 4.5 are:
      x ̈1 + 2*ω2*x1 − ω2*x2 = 0
      x ̈2 + 2*ω2*x2 − ω2*x1 = 0
    3. The attempt at a solution

    So the equations of motion with driving are :
    x ̈1 + 2*ω2*x1 − ω2*x2 = (Fd/m)*cos(2wt)
    x ̈2 + 2*ω2*x2 − ω2*x1 = (2Fd/m)*cos(2wt)

    I add and subtract the above differential equations and obtain:

    z'' + w^2 * z = (3Fd/m) *cos(2wt), where z = x1 + x2
    z'' + 3w^2 * z = (-Fd/m)*cos(2wt), where z = x1 - x2

    Then using z = Acos(2wt) and z = Bcos(2wt) as solutions to the above equations we end up with:
    A= -Fd/k and B=Fd/k.

    From here solving for x1 and x2 yields: x1 = 0 and x2 = (-Fd/k)*cos(2wt).
    This makes no sense to me, but it seems to be the only solution I'm getting.
     
  2. jcsd
  3. Nov 12, 2014 #2

    rude man

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    Homework Helper
    Gold Member

    For openers, using z to represent two different parameters is not a good idea.
    Also, you shoud have stated the original problem 4.35 in full.
     
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