Gareth's Downstairs Computer wrote on 8/5/2017 5:57 PM:
On 05/08/2017 22:24, rickman wrote:
Gareth's Downstairs Computer wrote on 8/5/2017 3:14 PM:
On 05/08/2017 20:06, rickman wrote:

Yes, because it *is* a PLL. In fact the problem most people have with it
is that it doesn't adjust the phase by adjusting the frequency of the
slave. It adjusts the *phase* so clearly it *is* a phase locked loop.

All pendulums have circular error where the frequency is determined by
the amplitude of swing,

All *uncorrected* pendulums have circular error. The Fedchenko clock has
a mounting spring for the pendulum that corrects for circular error.

Hadn't heard of that one. At the BHI lecture there was mention of
another correction of circular error by a colied spring attached
somewhere at the bottom, but I wasn't paying full attention at
that point.

There were also other means such as cycloidal cheeks around the
suspension spring.

so for the half cycle where the phase is adjusted by
abridging the swing by the hit of the hit and miss stabiliser, the frequency
of the slave is, indeed, changed.

This has nothing to do with the circular error.

It has everything to do with the circular error and the variation
in frequency that comes with varying amplitude of the swing.

You seem to be completely misunderstanding the operation of the Shortt
clock. The slave pendulum has no need for correction of circular error. It
is a good pendulum, but not a great one. It doesn't need to be great, it is
corrected every 30 seconds by the electromechanical escapement of the master
pendulum. It only has to be good enough to provide an appropriately timed
release of the gravity lever.

So the small circular error has no bearing on the slave pendulum.


The standard formula given for the cycle time of pendulums ..

2 * PI * root( L / G)

... is only valid for those small angles where sin( theta ) = theta,
and such angles are so infinitesimal that no visible movement
of a pendulum would be seen!

This equation is an approximation which ignores the higher terms of the
power series of the full equation. It is only truly valid for no swing at
all.

... which is virtually the range where sin( theta) = theta.

Exactly. This *is* the range where sin(theta) = theta. Anywhere other than
zero it is an approximation.

--

Rick C