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I finally computed the linear and non-linear solutions for the Cavendish experiment. The equation of motion is:

This is linearized as¹

The solution for initial condition t=0 and theta=0 is

C = GMmd

This is what I used to plot the linear line. Thanks again to Jean-Marc Gulliet for obtaining the solution in Maple and Mathematica. 

Non-linear solution was supplied by Robert Israel here.

I entered the values of the constants into excel and computed theta for every 10 seconds. The blue line shows the non-linear solution, red linear. Apparently the non-linear solution goes one full period (starts from middle point, or zero point, goes to maximum amplitude and comes back to zero point). The linear solution on the other hand appears to move from zero point to maximum amplitude. And amplitudes do not match either. Does this make sense to anybody?

These are the values of the constants:

> y = theta = excursion angle in radians
> A = I = moment of inertia = 13,138,117.34 g cm^2
> B = R = [not known at this point]
> C = k = torsion constant  = 724.68 g cm^2 sec^-2
> d = moment arm = 93.09 cm
> D = 2GMmd = 2 * 6.67*10^-8 * 158100 * 729.8 * 93.09 = 1432.82
> a = distance between weights = 22.10 cm

I would greatly appreciate any comments to make sense of what is going on here. Thanks.

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1. but see the comment here for different linear approximation. [↩]

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