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I have been trying to find a numerical solution to the non-linear differential equation describing torsion pendulum motion:

I y'’ + R y’ + K y = F / (a - y*d)^2

I = moment of inertia

R = damping constant

K = torsion constant

F = 2 GMmd

d = moment arm

y = theta = excursion angle 

(prime denotes time derivative of y)

I posted questions in several online places such as PlanetMath and AllExperts but could not work out the solution yet. Any help is appreciated.

But I also noticed that when y = 0 initially, we have

2GMmd/a^2 = 0

This is only possible if G = 0. This suggests to me that the differential equation does not properly describe the motion of the pendulum under the influence of the Newtonian force.

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