Pulley system with spring and car EOM

AI Thread Summary
The discussion revolves around deriving the equation of motion for a pulley system involving a spring and a car. The user describes their approach, which includes summing moments about the pulley and considering a frictionless environment. They express difficulty in arriving at the correct equation, specifically mentioning their current expression appears incorrect. The moment of inertia is noted to be at the center of the spring, and the spring is initially undeformed. The user seeks assistance to resolve their equation of motion problem.
tisquared
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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??
 

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tisquared said:
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??

Welcome to the PF!

I don't see the sketch yet -- try again to post it?
 
I am so sorry! Got it attached now
 
Bumping
 
anyone have any input? I really need some help :o(
 
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