# Does Cavendish pendulum have an occult motion?

If Newton’s force is occult and it does not exist in Nature how does the Cavendish pendulum move under the influence of the Newtonian force?

I claim that Cavendish pendulum does not move under the influence of the Newtonian force.

How can I prove this?

In Physics Forum we wrote down the Newtonian force exerted by the attracting weight as

F = G / (l – r)^2

And the restoring force or, torsion, of the wire as

T = kr

In modern derivations these two are equated

G/(l – r)^2 = kr

and solved for G.

G = Newton’s constant
k = torsion constant
l = is the distance between weights
r = the excursion of the pendulum arm

I first claimed that once the inverse square force is greater than the restoring force it would always be greater. But this is not the case. If we choose the constants G, k and l judiciously, we would get equal forces at some position, as Doc Al at Physics Forum showed.

Doc Al chose these values:

G = 1
k = 10
l = 1

Given these constants we have equality of forces at r = 0.13 and r = 0.59. ((Why two positions where forces are equal?))

I plotted the values of r in this spreadsheet.

I believe that in this case, where the forces are equal there is no stationary equilibrium. The arm keeps moving and after the second equality the force is always greater. This means that, in this scenario, the pendulum will hit the attracting weight without any stationary equilibrium happening.

What causes the arm of the pendulum to move is not the Newtonian force, but acceleration it imparts on the arm. And this acceleration is not constant. See the acceleration column (first differences) on the spreadsheet.

What are your thoughts on this? I would be grateful to anyone either commenting here or on Physics Forum or in this forum.

Some questions:

What is the equation of motion for the arm under the influence of the Newtonian force? I would think this would be something like (simple harmonic motion + acceleration caused by gravity).

Does the Newtonian force exert variable acceleration to the arm? I think so. In that case, since torsion force has constant acceleration it will never be able to counter the variable acceleration of gravity. Is this correct?

Many thanks.