Etude des effets non lin\'eaires observ\'es sur les oscillations d'un pendule simple

TL;DR

This study investigates the non-linear effects in a simple pendulum, focusing on anharmonicity, additional harmonics, and non-isochronism, especially at large oscillation amplitudes, using experimental measurements and curve fitting.

Contribution

The paper provides a detailed experimental analysis of anharmonic effects in a simple pendulum, highlighting the importance of precise curve fitting for accurate period measurement at large amplitudes.

Findings

Anharmonicity causes additional harmonics in oscillations.

The period of oscillation evolves quadratically with amplitude.

Detectable additional harmonics appear at high amplitudes.

Abstract

In this paper we present a study of the non-linear effects of anharmonicity of the potential of the simple pendulum. In a theoretical reminder we highlight that anharmonicity of the potential generates additional harmonics and the non-isochronism of oscillations. These phenomena are all the more important as we move away from the oscillations at small angles, which represent the domain of validity of the harmonic approximation. The measurement is apprehended by means of the acquisition box SYSAM-SP5 coupled with the Latis pro software and the Eurosmart pendulum. We show that only a detailed analysis by fitting the recorded curve can provide sufficient accuracy to describe the quadratic evolution of the period as a function of the amplitude of the oscillations. We we can detect the additional harmonics in the oscillations when the amplitude becomes very high.