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I want to compare linear and non-linear solutions of Cavendish experiment equation of motion:
1. Linear Solution without damping:
y(t) = A cos wt + B/w
w == omega_0^2 == omega_f (when there is no damping)
B = 2GMmd/Ia^2
2. The numerical solution for the non-linear version is given here as solved by Robert Israel in Maple.
For t=0 numerical solution has
y(0) […]

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 […]

What would physicists consider a necessary and sufficient evidence that Cavendish pendulum was not moved by Newton’s occult force which acts instantaneously from a distance?
What sort of evidence is required?
Historical

Analysis of original experiment without making anachronistic assumptions
Any experiment that is called Cavendish experiment

Mathematical

Cavendish’s original computation of delta, the mean density of the earth
Modern method to […]

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 […]

Newton defined force as the faith of his religion:
Force == Newton’s Soul
In the 19th century Newtonian priests defined the Cavendish experiment as the experimental proof of Newton’s Soul by defining the letter G as “Newton’s Universal Constant of Gravitation.” This was the greatest unification of physics:
Newton’s Soul is the universal cause of everything.
When the Newtonian […]

How does the pendulum arm move under the influence of F = GMm/s^2?
1. We know that F is not a contact force.
2. Force resides in M and travels the distance s and grabs the weight m from its center and attracts it toward itself.
3. The attractive actions of M described above happen in zero time. […]

It is well known that the computation of G from the Cavendish experiment is independent of weights m attached to the pendulum. The value of G given by the Cavendish experiment is the attraction between masses M and. The missing mass is substituted to save Newton’s authority.
G = 2 pi^2 r^2 s^2 theta / T^2 […]

Computing G from Cavendish data does not mean observing the Newtonian occult motion. We start from the principle that occult motion does not exist.
Occult motion is the same as perpetual motion.
Both are denied by principle.
Occult motion does not exist and it cannot be measured.
In physics Newton’s authority is absolute. Therefore, occult motion is legal in physics […]

Thanks to Edward Ruden who showed the error in my calculation commenting in sci.physics.research. Basically it is the same error mentioned by Carl Brannen in this comment.
The correct formula should be
G = k theta s^2 / 2Mml
We need to suppose that the torque acts on both extremity of the arm so that the torque is 2GMml/s^2.
There […]

Please take a look at this computation of G from the Cavendish experiment data. I have posted requests for comments at Physics Forum, sci.physics.research and to Cavendish Forum at Tangler. I would greatly appreciate comments.

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