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Equation of motion of coupled springs

  1. Jan 29, 2012 #1
    1. The problem statement, all variables and given/known data

    A system is connected as follows, going vertically downwards: (ceiling)-(spring with constant k)-(mass 1)- spring with constant k)-(mass 2)
    Let x be the displacement from the equilibrium position of mass 1, and let y be the displacement from the equilibrium position of mass 2. Take downwards displacement as positive.

    I'm trying to show that the angular frequencies of the normal modes are ω^2=(3±5)k/2m, but I'm stuck.

    m(d^2x/dt^2)=mg-kx
    m(d^2y/dt^2)=mg-k(y-x)

    When I try to put this into matrix form, I can't get rid of the mg terms.

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jan 29, 2012 #2

    vela

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    Note the bolded phrases. The mg terms shouldn't be there in the first place.

    By the way, I've moved this thread to the advanced physics forum since it looks like a problem from an upper-division classical mechanics course or math methods course.
     
  4. Jan 29, 2012 #3
    So I don't need the mg terms because they only affect the equilibrium position?
    So if I cross out those terms will the equations be right?
     
  5. Jan 29, 2012 #4

    vela

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    Right. When x=0, mass 1 is at its equilibrium position, so the net force on it is equal to 0. The same holds for mass 2 and (y-x)=0.
     
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