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Re: [Phys-l] mass and the ring down (free decay) of a pendulum

"But this may well increase the bob weight drag,
which should decrease Q. Hence the decay constant of a pendulum
should not be independent of its mass."

The experimenter (1) was "smarter" than that. He changed the density (2), using the same volume".

Another matter I discuss in an article I wish to submit soon is the escapement energy is not constant w/ amplitude. That was the motivation for my previous request about the small mass on the wedge. Working w/ Synchronomes is a "pain" and a "joy" (3) because their Q is very approximately, 10K. Escapement energy is in the order of a few dynes and only twice a minute! These clocks typically vary seconds a month or less.
I've examined the change in moment of inertia and in the spring suspension pivot point; both negligible compared to the effect of the mass. Mentioned, but not estimated (modelled), is the loss (hysteretic) from vibration of the rod when escapement impulsed. Since I suspect the rod is "more rigid" w/ greater tension (increased mass), this would reduce that loss counteracting the support loss effect.

Regarding the Pasco lab. I have a photogate system (4) that is considerably more accurate than theirs, also the majority of pendulua supplied by Pasco (5) and similar firms are likely not suitable as their support losses will likely swamp the Q variation predicted by the model. A possible exception is the Leybold wherein the suspension is screwed into a wooden beam w/ a large knife edge screw. (6) Another possible method would be to use rather initially low mass bobs, as the effect possibly is non-linear at low mass. From Heldman's data, I found the effect (steady state amplitude) not quite linear. [A ~ 46.0 -1.53M + 0.0452M^2]

I'll reply to JD in another post.

bc

(1) Heldman, Alan; Horological Science Newsletter issues: 2006-5 and 2007-1.
(2) Tungsten, brass, iron, and mixed iron and aluminium. The last because the purely Al bob's equilibrium amplitude was so large it bumped either clock parts or the case, forgot which. Masses from about 15 to 4 kg.
(3) Difficult to model -- Very sensitive to factors one ignores when teaching, even in an advanced UG lab.
(4) http://www.bmumford.com/clocks/index.html
(5) http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=53926&Detail=1 <http://store.pasco.com/pascostore/showdetl.cfm?&DID=9&Product_ID=53926&Detail=1>
(6) Two dimensional support KEP catalogue # 346 39; Needle suspension not as good as I though. Referenced: Nelson and Olsson, Am. J. Phys. 54 p. 112



bc



Brian Whatcott wrote:

At 11:09 AM 6/9/2007, you wrote:

PHYS-L, PHYSHARE, and TAP-L, people!

There is a controversy among the horological community on the effect of
pendulum mass on the steady state amplitude of an escapement driven
clock, in particular the impulsing by the gravity arm of a Synchronome
clock. Theoretically for a simple pendulum clock with a decay constant


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decrease Q. Hence the decay constant of a pendulum
should not be independent of its mass.
As to experimental data - this is the grist of engineering labs
such as this one:

<http://www.physics.odu.edu/hyde/Teaching/Fall04/Lectures/ResonanceLab.html>


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