Effect of a spring on equations of motion

AI Thread Summary
A torsional spring with constant K will primarily influence the moment equation in the equations of motion by introducing an additional term K(theta). Its placement at the connection between the pendulum and cart means it exerts forces on both components. The spring's effects on the cart and rod need to be considered in the overall force analysis. Reaction forces related to the spring's impact may be addressed through the parameters P and N outlined in the referenced material. Understanding these dynamics is essential for accurate modeling of the system's behavior.
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Homework Statement


I am just wondering what effect a torsional spring, with constant K, would have on the equations (1) to (5), under the section "Force analysis and system equations". The torsional spring is located where the pendulum and cart are connected
http://ctms.engin.umich.edu/CTMS/index.php?example=InvertedPendulum&section=SystemModeling

Homework Equations

The Attempt at a Solution


I think it would only affect the moment equation, with an extra term K(theta)?
 
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Wouldn't the spring be attached to the cart? And thus exert a force on the cart as well as the rod?
 
BiGyElLoWhAt said:
Wouldn't the spring be attached to the cart? And thus exert a force on the cart as well as the rod?

i don't know what forces are involved, wouldn't those just be reaction forces covered by P and N on the website
 

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