An asymmetric isochronous pendulum

Abstract

In this work, we propose a novel asymmetric isochronous pendulum, where half of the trajectory corresponds to that of the (non-isochronous) simple pendulum, while the remaining part corresponds to a specific trajectory. The pendulum's complete swing is isochronous—i.e., its period is not dependent on the oscillation amplitude. This new design is inspired by the symmetric isochronous Huygens pendulum, in which the trajectory is modified by cycloidal guides. In our case, only one guide is needed, for which analytical expressions are given for the first time. The objective of the paper is to add a new pedagogical tool in the undergraduate-level physics courses for understanding the isochronism concept, specifically the time delay for large amplitudes in the simple pendulum must be compensated by accelerating it along the new trajectory. We also introduce a novel numerical method to find the trajectory, based on the convergent superposition of straight trajectories (inclined-plane type) to approximate the curve. The procedure is not only accurate, but it is also appropriate for introducing the concepts of differential calculus and inclined-plane mechanics.

CDIO‐CT collaborative strategy for solving complex STEM problems in system modeling and simulation: An illustration of solving the period of mathematical pendulum

“…As an improvement of MP, C. Huygens proposed the concept of symmetric isochronous pendulum. Recently, Randazzo et al proposed the asymmetric isochronous pendulum for the first time [29, 30]. The discussion of isochronous pendulum is an extension of this work on MP and the computation of the period will be a new evolution, which could be a new project for the students.…”

Different approaches and methods for solving oscillator problems

“…In particular, a system of massive balls connected by springs is the simplest model of molecular and crystal structures. Teaching different approaches and methods of solving the problems expands the student's set of tools, helps to avoid mistakes by verifying the result in another way, provides a better and more complete understanding of the physics phenomenon, and improves both the technique and physical intuition [5][6][7].…”

Isochronous space–time wave packets

“…A different strategy is to search for isochronous (or equal-time) configurations. One example is Huygens' isochronous pendulum, which is built on the discovery that a particle sliding on a cycloid (or tautochrone curve) returns after a fixed time interval independently of point of release [2,3]. However, this strategy has had less impact in optics.…”