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.(adsbygoogle = window.adsbygoogle || []).push({});

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??

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# Pulley system with spring and car EOM

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