Nonisochronism in the interrupted pendulum

Gil, Salvador; Gregorio, Daniel E. Di

doi:10.1119/1.1578071

Cited by 3 publications

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References 4 publications

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“…The systems we will discuss can also be used to establish a connection between classical isochronism and the quantum mechanical equal spacing of the energy levels in a harmonic oscillator. 1 The motion of a particle can be used to investigate the consequences of nonlinear effects in an oscillatory system.…”

Section: Introductionmentioning

confidence: 99%

Perturbation of a classical oscillator: A variation on a theme of Huygens

Gil

Gregorio

2006

American Journal of Physics

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Simple, simpler, simplest: Spontaneous pattern formation in a commonplace system Am. J. Phys. 80, 578 (2012) Determination of contact angle from the maximum height of enlarged drops on solid surfaces Am. J. Phys. 80, 284 (2012) Aerodynamics in the classroom and at the ball park Am. J. Phys. 80, 289 (2012) The added mass of a spherical projectile Am.The motion of a particle in different potentials is investigated theoretically and experimentally. The dependence of the period of oscillation on the amplitude is studied for pendula associated with some of these potentials. A technique is proposed to modify the trajectory of a pendulum bob so that it moves along a predetermined curve, and a simple and low cost experiment to study the relation between the period and amplitude for different potentials is discussed. We report on the motion of several pendula whose periods decrease with increasing amplitude. In particular, we study the effects of a perturbation of the form z 4 on the frequency of oscillation of a simple harmonic oscillator. Our results agree with the expectation that any perturbation of a simple harmonic oscillator destroys its isochronism.

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Section: Introductionmentioning

confidence: 99%

Perturbation of a classical oscillator: A variation on a theme of Huygens

Gil

Gregorio

2006

American Journal of Physics

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Detecting anharmonicity at a glance

et al. 2014

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Harmonic motion is generally presented in such a way that most of the students believe that the small oscillations of a body are all harmonic. Since the situation is not actually so simple, and since the comprehension of harmonic motion is essential in many physical contexts, we present here some suggestions, addressed to undergraduate students and pre-service teachers, that allow one to find out at a glance the anharmonicity of a motion. Starting from a didactically motivated definition of harmonic motion, and stressing the importance of the interplay between mathematics and experiments, we give a four-point criterion for anharmonicity together with some emblematic examples. The role of linear damping is also analysed in relation to the gradual changing of harmonicity into anharmonicity when the ratio between the damping coefficient and the zero-friction angular frequency increases.

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An asymmetric isochronous pendulum

Randazzo

Ibáñez

Rosselló

2018

American Journal of Physics

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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.

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Nonisochronism in the interrupted pendulum

Cited by 3 publications

References 4 publications

Perturbation of a classical oscillator: A variation on a theme of Huygens

Perturbation of a classical oscillator: A variation on a theme of Huygens

Detecting anharmonicity at a glance

An asymmetric isochronous pendulum

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