Gareth's Downstairs Computer wrote on 8/6/2017 1:37 PM:
On 06/08/2017 17:18, rickman wrote:
Gareth's Downstairs Computer wrote on 8/6/2017 5:26 AM:
On 05/08/2017 23:25, rickman wrote:
You seem to be completely misunderstanding the operation of the Shortt
clock. The slave pendulum has no need for correction of circular error.

I'm sorry, but you totally misunderstood what I was saying, which was
that because all pendulums exhibit circular error, when the hit occurs
in the hit and miss synchroniser and foreshortens the swing, then, for
that half-cycle, and only that half cycle, the frequency is
changed, as it must be.

Just as in the electronic PLL, instantaneous changes of phase have
instantaneous changes of frequency, no matter how short lived,
associated with them.

What you say about frequency vs. phase is true and how the Shortt clock
adjusts phase, but it has nothing to do with circular error of the
pendulum. The correction of the phase is from the added spring resistance
shortening the time as well as the travel of the pendulum. The fact that
the swing is shorter and the second order circular error will create a
tiny error in the timing is pretty much irrelevant. The real change is
from the added spring constant changing the first order effect in the
pendulum equation. The coefficient of the gravitational constant is
effectively changed by the spring.

Is that more clear?


You continue to misunderstand. Any pendulum swinging with circular error
speeds up for shorter amplitude; speeding up means increased frequency.
Therefore, for the half cycle inwhich there is a hit, a shorter amplitude
and hence instantaneous higher frequency exists.

I understand perfectly and explained it for you in excruciating detail. The
change in phase of the Shortt clock slave pendulum is due to the FIRST ORDER
change in the effective gravitational constant in the pendulum equation by
engaging the leaf spring. While the reduced amplitude of the swing *will*
cause a SECOND ORDER effect in the motion of the pendulum, it will be MUCH
SMALLER than the FIRST ORDER effect.

What part of this do you not understand or not agree with?

--

Rick C