Another look at a damped physical pendulum

Simbach, John C.; Priest, Joseph

doi:10.1119/1.1858488

Cited by 30 publications

(28 citation statements)

References 8 publications

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“…That straight-line fit has been reproduced as the solid curve in figure 1 over the same horizontal and vertical axis ranges used in [1]. However, in another recent paper [3] which referenced previous work on the damping of a physical pendulum [4], the frictional torque at an axle was instead assumed to be constant, independent of the angular speed of motion, for as long as the system is rotating. If this expression is substituted into equation 2 as the dashed curve using this value of a/I.…”

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confidence: 76%

Frictional torque on a rotating disc

Mungan

2012

Eur. J. Phys.

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Resistance to motion often includes a dry frictional term independent of the speed of an object and a fluid drag term varying linearly with speed in the viscous limit. (At higher speeds, quadratic drag can also occur.) Here, measurements are performed for an aluminium disc mounted on bearings that is given an initial twist and allowed to spin until it comes to a stop. It is found that a sum of both the dry and fluid resistive terms are needed to accurately fit the entire data. However, the speed-independent term alone suffices over any suitably limited range of motion, permitting one to use the standard kinematic equations for constant angular acceleration. The measurements and theory are appropriate for an introductory physics laboratory at the college level.

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confidence: 76%

Frictional torque on a rotating disc

Mungan

2012

Eur. J. Phys.

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“…The role of Coulombic dry friction in the damping of the harmonic motion of a small solid object on a substrate or that of a pendulum has been known for quite some time. − Most recently, the difference between Coulombic dry friction and kinematic friction was clearly demonstrated in an elegant experiment by Simbach and Priest, who studied the swinging of a pendulum, the pivot of which is a rotary variable resistor. As the pendulum swings, a Coulombic friction operates inside the variable resistor.…”

Section: Introductionmentioning

confidence: 99%

Experimental Investigation of the Drift and Diffusion of Small Objects on a Surface Subjected to a Bias and an External White Noise: Roles of Coulombic Friction and Hysteresis

2009

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We study the stochastic motion of a small solid block or a small water drop on a flat solid support in the presence of an external noise and a bias. The bias is caused either by inclining the plane of the support, as is the case with the solid block, or by creating a gradient of wettability, as is the case with a water drop. Both the solid block and the water drop exhibit drifted Brownian-like motion. There are, however, differences between the motion described here and that of a classical drifted Brownian motion, in that the Coulombic friction (for solid on solid) or wetting hysteresis (for water drops on a solid) accounts for a significant resistance to motion in addition to the kinematic friction. Although the displacement distribution here is non-Gaussian, the variance of the distribution increases with time, indicating that the overall motion follows simple diffusion. The diffusivity and the mobility of the solid object are considerably lower than the values expected when the diffusion is governed by only kinematic friction. The experimental diffusivity increases with the power of the noise with an exponent of 1.61, which is close to that (1.74) of an analysis based on the Langevin equation when the Coulombic friction is taken into account in addition to the kinematic friction. The ratio of diffusivity and mobility increases slightly sublinearly with the power of the noise with an exponent of about 0.8. The experimentally observed relaxation time of the process is, however, considerably smaller than the Langevin relaxation time. When the experimental ratio of diffusivity and mobility is taken into account in the distribution function of the displacement, the later quantity becomes amenable to an analysis that is similar to the conventional fluctuation relations.

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“…which indicates a parabolic decay trend. Figure 5 depicts the energy step-like decay according to the exact solution, the best-fit approximate solution (5), as well as the parabolic trend line (6). Again note the excellent agreement between the exact and approximate decay curves, particularly at the turning points where the two flatten out.…”

Section: Energy Decaymentioning

confidence: 85%

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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Another look at a damped physical pendulum

Cited by 30 publications

References 8 publications

Frictional torque on a rotating disc

Frictional torque on a rotating disc

Experimental Investigation of the Drift and Diffusion of Small Objects on a Surface Subjected to a Bias and an External White Noise: Roles of Coulombic Friction and Hysteresis

Revisiting the Coulomb-damped harmonic oscillator

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