Brian Reay wrote on 8/5/2017 5:10 PM:
On 05/08/17 20:14, Gareth's Downstairs Computer wrote:
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, 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.


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!



You seem to be confusing two different things

The error you refer to is due to the pendulum not actually taking a direct
line between the ends of its travel, the error is small for small
amplitudes. There was a famous experiment by a Frenchman in, I think Paris,
he hung a huge pendulum and let it trace its path in sand, rather than it
going 'to and fro' it actually went in arcs as it went to and fro.

The effect is minimised by reducing the amplitude.

I believe you are thinking of the Foucault pendulum. This had nothing to do
with elliptical paths of pendulums. This was a pendulum free to swing along
any axis. As the earth rotates the pendulum continues to swing in its
original path and the earth turns beneath it. Of course the pendulum
appears to rotate the plane of swing.


As you correctly say, the frequency of a pendulum is given by the formula
you state. If you 'give it a nudge' you may shorted one swing but the
overall frequency is still determined by the formula.

The 'nudge' will change the phase of the swing, not the frequency- ie it
will shorten one cycle.

Yes, that is right. The change in frequency (phase change rate) is only
momentary.

--

Rick C