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Pulley system with spring and car EOM

  1. Oct 1, 2010 #1
    Hi all! I am working with a problem that for the life of me am having the hardest time with deriving the equation of motion. I have attached the sketch to give a better representation.

    The moment of inertia, J, is at the center of the spring. No friction between car and table and cables do not slip, so no friction there either. The spring is undeformed when the system is in static equilibrium.

    This is how far I have gotten so far, but it is wrong:
    Summing the moments about the center of the pulley and assuming frictionless surface for the block I get the following expression:
    m = mass of block

    m*r - F(spring)*R = J*theta-doubledot + m*a(acceleration of block towards x)*r
    plugging in F(spring) = k*r*theta and a = r*theta-doubledot I get the following
    theta-doubledot + ((k*r*R)/(J+m*r^2))theta - (m*r)/(J+m*r^2)

    Can anyone please help me??

    Attached Files:

    Last edited: Oct 1, 2010
  2. jcsd
  3. Oct 1, 2010 #2


    User Avatar

    Staff: Mentor

    Welcome to the PF!

    I don't see the sketch yet -- try again to post it?
  4. Oct 1, 2010 #3
    I am so sorry! Got it attached now
  5. Oct 1, 2010 #4
  6. Oct 2, 2010 #5
    anyone have any input? I really need some help :eek:(
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