Re: [Phys-l] Discrepant amplitude measurement

[brian whatcott <betwys1@sbcglobal.net>]

On 8/3/2011 3:47 PM, Bernard Cleyet wrote:
> The horological community principally uses two methods to find the amplitude of a pendulum -- one is an obvious use of the work energy theorem. i.e. measure the speed at the equilibrium position (Bottom Dead Centre), the other the time the pendulum is "beyond" the photogate placed near the maximum displacement.  This method is claimed to be more sensitive and a more direct measure of the amplitude (It's been compared to visual measurements.)
>
> These methods are however discrepant when a magnetic field is used to simulate a changed g, i.e. to imitate the changing g due to the relative position of the moon.
>
> Unfortunately, one cannot use a space constant magnetic field to change the force on a pendulum with a bob containing a PM.  This, I surmise, is why the measurements differ.  The time beyond the photogate requires pendulum sinusoidal motion and the W-E method requires a high Q.  (The pendulum must not lose much energy during a single half cycle.) Neither occur using this simulation method. The displacement is not sinusoidal because the force is not constant, and I think the Q is reduced by the magnetic method, because of eddy currents, and the Faraday effect in the coil driven by a low Z source.
>
> I will appreciate comments.
>
> bc horological amateur.
>
>
> The discrepant method article:
>
> http://www.cleyet.org/Pendula,%20Horological%20and%20Otherwise/The%20Littlemore%20clock%202.pdf
bc was endorsing a hi-point dwell-time pendulum amplitude sensing  
approach as more compatible with gravity vector variation from tidal 
forces than the pendulum bob  mid swing velocity measurement 
alternative  that a cited clock uses.

I like this approach, if only because it closely replicates the Shortt 
pendulum sensing method, which drops a sense lever if the amplitude is 
too great, but actuates an electromagnet if the amplitude decays so that 
the sense lever is not dropped, but instead, closes a contact.

I am not quite so enthusiastic about the justification - that mid cycle 
velocity control allows amplitude to vary with effective g,
whereas amplitude control means varying energy is input with varying 
g.    Why should controlling for constant energy be more noisy than 
controlling for constant amplitude?    Certainly, the non-linearity 
inherent to the sine approximation depends on the amplitude - but the 
noise in question occurs at gravitationaly quiet times.

Brian W