Barometric Compensation of a Pendulum

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.