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Two Springs and Two Masses. Equation of Motion

  1. Feb 1, 2010 #1
    1. The problem statement, all variables and given/known data
    Derive the equation of motion for the following Mechanical System. You need to introduce an additional variable to represent position of the bottom mass.

    I drew a picture ;D

    2. Relevant equations

    Mx(double Dot) = reactionary forces

    Bx(dot) is the damping effect: B = damping coefficient times the velocity

    3. The attempt at a solution
    Now, this is apparently a vibration type problem. But I'm assuming too many things when trying to write the Eq. of Motion.. so I don't feel confident about the question. When the K1 spring is pulled towards the right, M1 stars moving towards the right... Obviously.. Now, a few questions come up, the figure assumes that M2 has a direction to right ( Atleast I think.. thats the Xout in the picture). So what does that mean? The friction between M1 and M2 is static friction so M2 does not slide and just moves to the right until spring K2 pulls it back and then Kinetic friction comes in.

    But I was told by a few people, to not think of this as having friction but actually like the masses are damping each others velocities. So the Eq. Of Motion would have Bx(dot) instead of a couple of Kx.

    I just need a little bit of direction on this problem.

    Heres what I have come up with.

    Assuming M2 slides the opposite way as M1 moves to the right. So M2 basically oscillates back and forth just a tiny bit as the bigger mass M2 moves right and left.

    So that means that the two masses provide a damping effect on each other.

    So if i was to write the EOM: [ displacements have to be defined in the figure obviously so just assume that I defined them right]

    (M1 + M2)x(double dot) = K1(X3 - X2) - Bx(dot) - Bx(dot) - K2(Delta S)

    But I'm not confident about this because I'm not sure I get the whole scenario conceptually.

    Thanks For The Help!
  2. jcsd
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