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[Phys-L] Pendulum drive.



Before this pendulum thread does its seven-year cicada dive  into the silent roots, I thought I would leave something for the next person who develops an interest in pendulum clocks.Long-case clocks are usually driven by constant impulse per beat escapements. This impulse is above the center of percussion, above the center of mass and above the radius of gyration(aka oscillation). This imports some lateral oscillation which requires enough stiffness to mimimize spectrum spreading of the impulse driven pendulum.This has been mitigated by applying the impulse over a longer portion of the arc, with a gravity ramp escapement used less frequently than once per beat ( say once in thirty cycles of the  Shortt-Synchronome) but ideally applied throughout the cyclePendula are subject to length and amplitude variations. Length can be controlled in a thermostatic enclosure, selection of low thermal coefficient materials like Invar or Fused quartz or complementary lengths of  metals of different thermal coefficients or a mercury-fil column in a judiciously sized narrow container. Reduction of atmospheric pressure variation can be provided by an an enclosure at constant, preferably low-pressure
Lateral vibrations can be eliminated, and the spectral purity of the pendulum's beat  can be further enhanced by a parametric drive.  (This has the effect of replacing frictional resistance with a reactance which reduces the drive noise contribution to the spectrum.)
This then permits the option of reducing the pendulum to "simple" form e.g. with a small bob on a fused quartz thread, where the beat is sensed photo-electrically at the bob.The parametric drive can be arranged using piezo-crystals or piezo-ceramics at the suspension point. These materials can provide a 1 part per thousand length variationThe amplitude of the  sinusoidal pumping drive can be modulated by sensing swing amplitude suitably, though the rate of changing pumping amplitude is best varied slowly during multiple cycles.
A splendid project for a Science Fair, I think. A worthy target would be an error of less than 1 second per year. (Better by far than a Rolex wrist-watch)