Abstract
The Foucault pendulum provides a demonstration of the turning of the Earth. The principle at work is that linear oscillations of a two-degree-of-freedom isotropic harmonic oscillator remain unchanged in an inertial frame of reference, so appear to precess in a rotating frame of reference. In recent work, we applied two-degree-of-freedom isotropic oscillators to mechanical timekeeping. In this paper, we note that the spherical oscillators we considered have qualitatively different behavior in a non-inertial frame. We show that when in a rotating frame, linear oscillations precess at one half the rotational speed of the rotating frame. We validate this result experimentally by designing and constructing a proof of concept demonstrator placed on a motorized rotating table. The demonstrator consists of a spherical isotropic oscillator, a launcher to place the oscillator on planar orbits, a motorized rotating table, video recording for qualitative observation, and a laser measurement setup for quantitative results. The experimental data recorded by the lasers strongly validate the physical phenomenon.
Highlights
The Foucault pendulumIn 1851, Léon Foucault created a sensation with his pendulum providing a direct demonstration of the turning of the Earth; for a historical description, see Refs. 4 and 15
The goal being to study the behavior of the spherical oscillators with strictly linear oscillations when placed in a vertically rotating frame, the demonstrator consists in an oscillator, a measurement system, a device capable of putting the oscillator into rotation, and a system to launch it on linear orbits
This paper gives an analytical argument showing that linear orbits of 2-DOF spherical oscillators, when put in a rotating frame, precess at half the angular speed of the rotation
Summary
In 1851, Léon Foucault created a sensation with his pendulum providing a direct demonstration of the turning of the Earth; for a historical description, see Refs. 4 and 15. Our EPFL laboratory has considered harmonic isotropic 2-DOF oscillators applied as time bases for mechanical timekeepers, with results communicated in a series of papers.. The advantage of using these time bases is that they no longer need the complex escapement mechanism required in all previous mechanical timekeepers. The specifications for such harmonic isotropic 2-DOF oscillators to be mechanical time bases are the following: 1. Our basic contribution was to note that this isochronism means that the oscillator can be used as a time base for an accurate timekeeper and that unidirectional orbits eliminate the need for a classical escapement mechanism. Note that condition 9 applies only to portable timekeepers such as watches but not to clocks
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