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Brian!
Not quite my problem. I'm not using a clock w/ a "driving"
escapement.* I'm trying to explain the ("instantaneous")** change
in amplitude when a portion of the bob falls from a freely decaying
pendulum. I do find changes in the Q, because I fit to an
exponential decaying amplitude to find the amplitude. [decay
constant ~ 0.003) This "study" was prompted by my friend's
failure to detect a change in amplitude (measured by the flag
interrupt time at BDC of a photogate) when "sliding off" three
quarters (0.02kg) from a 77 kg tower clock's bob. *** [Easily
explained by the minuscule mass (0.02kg) compared to the bob's, and
the detector's insensitivity.] I find significant changes in
amplitude using a rotary motion detector as the suspension and
electromagnetically dropping a 0.07kg mass from a 0.30kg pendulum
(rod 0.025kg).
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pics here:
http://www.cleyet.org/Horological/weight%20pan%20effect/
I've just increased the mass dropped for further trials from 0.07
to 0.120kg.
---------------------
Your discussion is well known to horologists (centuries), and is
complicated by support loss. A few years ago an horologist (AH)
did a study exactly as you describe w/ constant size using W,
brass, steel and Al. (IIRC) The expected Q increase w/mass did not
occur, because of the increased support loss even when the support
(many kg cast iron) was bolted to a concrete column. In the
clock's wood case the clock failed to operate w/ the W bob! He
measured the motion of the support, inter alia, using a light
lever.
I reported this back in '07:
https://carnot.physics.buffalo.edu/archives/2007/06_2007/msg00024.html
n.b. my confusion of force and E.
* Not incidentally, the better clocks vary the drive to maintain
constant amplitude as part of the method of mitigating circular
error. e.g. the Synchronome and Littlemore. I don't remember what
Woodward did w/his clocks.
** Now I understand the cause of the confusion. I shoulda writ
originally "instantaneous change" not implied a change in the
change (decay) of the amplitude when part of the bob drops.
*** there's another problem here. If the photogate did detect a
change in amplitude, it would not be correct unless the mass'
original position was above the C of M of the bob. Otherwise,
there would be an unintended torque change and the position of BDC
would change. I position my added mass on the electromagnet so that
BDC doesn't change.
bc
p.s. Indeed, the decay constant does increase for the 0.12kg drop
from 0.00239 to 0.00278 Using the usual assumptions (i.e. linear
dissipation and decay constant <<
1) Q = angular frequency / 2(decay constant), my result is: before
drop, Q= 1076 and after, Q = 944