Sliding friction and the harmonic oscillator

Barratt, C.; Strobel, George L.

doi:10.1119/1.12495

Cited by 25 publications

(14 citation statements)

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“…In the interesting case of sliding friction, it can be demonstrated that a constant friction force does not affect the frequency of a simple harmonic motion, but only the amplitude of oscillation, which is decreased each cycle [11,12]. Therefore sliding friction cannot produce an amplitude dependence of the oscillation period.…”

Section: Damped Oscillationsmentioning

confidence: 99%

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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Section: Damped Oscillationsmentioning

confidence: 99%

Detecting anharmonicity at a glance

et al. 2014

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“…Barratt and Strobel treated a mass-spring system with dry friction on an inclined plane, with a driving force that allows acceleration up and down the plane with different magnitudes. 2 Squire considered a rigid pendulum with dry friction and linear and quadratic viscous forces. 3 He also discussed experimental procedures for equipping the pendulum such that one of the damping mechanisms would be dominant.…”

Section: Introductionmentioning

confidence: 99%

Negative Coulomb damping, limit cycles, and self-oscillation of the vocal folds

Fulcher

Scherer

Melnykov

et al. 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.An effective one-mass model of phonation is developed. It borrows the salient features of the classic two-mass model of human speech developed by Ishizaka, Matsudaira, and Flanagan. Their model is based on the idea that the oscillating vocal folds maintain their motion by deriving energy from the flow of air through the glottis. We argue that the essence of the action of the aerodynamic forces on the vocal folds is captured by negative Coulomb damping, which acts on the oscillator to energize it. A viscous force is added to include the effects of tissue damping. The solutions to this single oscillator model show that when it is excited by negative Coulomb damping, it will reach a limit cycle. Displacements, phase portraits, and energy histories are presented for two underdamped linear oscillators. A nonlinear force is added so that the variations of the fundamental frequency and the open quotient with lung pressure are comparable to the behavior of the two-mass model.

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“…Introducing the new variable X = x ∓ f /k, we see from (1) that between any two consecutive turning points the motion is simple harmonic, of period T = 2π m/k, about an equilibrium position displaced by a fixed amount f /k against the motion (see e.g. [17]). It follows that the time it takes to go from one turning point to the next (half a cycle) is a constant equal to half the period of the undamped oscillator.…”

Section: Overview Of Coulomb Dampingmentioning

confidence: 99%

Revisiting the Coulomb-damped harmonic oscillator

Rizcallah¹

2019

Eur. J. Phys.

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The force of dry friction is studied extensively in introductory physics but its effect on oscillations is hardly ever mentioned. Instead, to provide a mathematically tractable introduction to damping, virtually all authors adopt a viscous resistive force. While exposure to linear damping is of paramount importance to the student of physics, the omission of Coulomb damping might have a negative impact on the way the students conceive of the subject. In the paper, we propose to approximate the action of Coulomb friction on a harmonic oscillator by a sinusoidal resistive force whose amplitude is the model's only free parameter. We seek the value of this parameter that yields the best fit and obtain a closed-form analytic solution, which is shown to nicely fit the numerical one.

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Sliding friction and the harmonic oscillator

Cited by 25 publications

References 0 publications

Detecting anharmonicity at a glance

Detecting anharmonicity at a glance

Negative Coulomb damping, limit cycles, and self-oscillation of the vocal folds

Revisiting the Coulomb-damped harmonic oscillator

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