Freedom of Science

I’ve been working on the equation of motion for the Cavendish pendulum. The motion is similar to torsional harmonic oscillator equation but with the addition of torque term for gravity 2GMmd/(a-x)^2.

My source is this document. The solution is based on the assumption that the excursion of the arm x is much smaller than the distance between weights a and therefore we can simplify this expression by saying that x = d theta << a.

I am looking to find the solution without making this simplification so that the force (or torque) varies as it should by the varying distance.

Thanks for helping.

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