Effect of a spring on equations of motion

[theone]

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)?

 

[BiGyElLoWhAt]

Wouldn't the spring be attached to the cart? And thus exert a force on the cart as well as the rod?

 

[theone]

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