Design of a Flexure Based Low Frequency Foucault Pendulum

Abstract

Abstract The Foucault pendulum is a well-known mechanism used to demonstrate the rotation of the Earth. It consists in a pendulum launched on linear orbits and, following Mach’s Principle, this line of oscillation will remain fixed with respect to absolute space but appear to slowly precess for a terrestrial observer due to the turning of the Earth. The theoretical proof of this phenomenon uses the fact that, to first approximation, the Foucault pendulum is a harmonic isotropic two degree of freedom (2-DOF) oscillator. Our interest in this mechanism follows from our research on flexure-based implementations of 2-DOF oscillators for their application as time bases for mechanical timekeeping. The concept of the Foucault pendulum therefore applies directly to 2-DOF flexure based harmonic oscillators. In the Foucault pendulum experiment, the rotation of the Earth is not the only source of precession. The unavoidable defects in the isotropy of the pendulum along with its well-known intrinsic isochronism defect induce additional precession which can easily mask the precession due to Earth rotation. These effects become more prominent as the frequency increases, that is, when the length of the pendulum decreases. For this reason, short Foucault pendulums are difficult to implement, museum Foucault pendulum are typically at least 7 meters long. These effects are also present in our flexure based oscillators and reducing these parasitic effects, requires decreasing their frequency. This paper discusses the design and dimensioning of a new flexure based 2-DOF oscillator which can reach low frequencies of the order of 0.1[Hz]. The motion of this oscillator is approximately planar, like the classical Foucault pendulum, and will have the same Foucault precession rate. The construction of a low frequency demonstrator is underway and will be followed by quantitative measurements which will examine both the Foucault effect as well as parasitic precession.