If you attach torsion spring to inverted pendulum is this, Mechanical Engineering

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If you attach torsion spring to inverted pendulum is this

If you attach torsion spring to inverted pendulum, is this the equation of motion? The spring is attached on one end to a pivot point and also at the pivot point the spring is attached. I used L/2 for the location of the center of mass.

I*theta"+mg(L/2)sin theta-theta*k=0

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