Affiliation:
1. Hyperbolic Consulting, Cedar Crest, NM, 87008
Abstract
Abstract
For centuries, accurate pendulum clocks were of strategic scientific and military importance. Environmental factors such as temperature and pressure affect the rate of a pendulum. Without temperature compensation, accuracy is limited to about 10 s per day. With it, however, a secondper month is possible. Barometric compensation is required for additional improvement. Indeed, highly accurate pendulum clocks, such as Shortt-Synchronome Pendulums, are placed in controlled partial vacuums to avoid this unsolved problem. We model the pendulum as a Duffing oscillator to account for the effects of circular deviation, buoyancy, virtual mass, and aerodynamic drag. The application of routine perturbation methods reveals a simple and elegant solution to the problem of barometric compensation, an arc of motion where a balance is achieved. The results are confirmed by comparison to experiment.
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
1 articles.
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