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Randall D. Peters

Publications and source records attributed to Randall D. Peters.

At least 37 records · Page 2Linked to original sources

Mesoscale Quantization and Self-Organized Stability

In the world of technology, one of the most important forms of friction is that of rolling friction. Yet it is one of the least studied of all the known forms of energy dissipation. In the present experiments we investigate the oscillatory free-decay of a rigid cube, whose side-length is less than the diameter of the rigid cylinder on which it rests. The resulting free-decay is one of harmonic motion with damping. The non-dissipative character of the oscillation yields to a linear differential equation; however, the damping is found to involve more than a deterministic nonlinearity. Dominated by rolling friction, the damping is sensitive to the material properties of the contact surfaces. For `clean' surfaces of glass on glass, the decay shows features of mesoscale quantization and self-organized stability.

physics.gen-ph↗

Spice Modeling of the Vilnius Chaotic Oscillator

``A simple chaotic oscillator for educational purposes'' was recently described in the literature [1]. In addition to their hardware description, the authors of this paper generated a bifurcation diagram from the model equations presented in their paper. In the present treatment of their circuit the `simulation program for integrated circuit engineering' (Spice) has been used to generate some insightful graphs that were not shown by the Lithuania group.

physics.ed-ph↗

The Yo-yo Oscillator (Analysis of a Nonlinear System using Spice)

Unlike the simplest (Hooke's law spring) oscillator, where the restoring force is in magnitude proportional to the displacement; the yo-yo oscillator has a constant force-magnitude. In other words, its potential energy function is linear, as contrasted to the quadratic (harmonic) potential of the simple harmonic oscillator. The linear potential is responsible for a nonlinear equation of motion which yields many surprising solutions. Rich in complexity, these solutions are in some cases chaotic. Numerical solutions to the equation of motion are presently obtained using the 'simulation program for integrated circuit engineering' (Spice). The circuit employed involves operational amplifiers and solid state switches.

physics.ed-ph↗

Beyond the Linear Damping Model for Mechanical Harmonic Oscillators

The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook exponential, the steady state behavior of the instrument for sub-resonance drive can be remarkably complex. Although the response cannot be explained by linear damping models, the general features can be understood with the nonlinear, modified Coulomb damping model developed by the author.

physics.class-ph↗

Spreadsheet Filtering by FFT Gaussian-based Convolution

Filtering of digital signals is accomplished on an Excel spreadsheet using fast Fourier transform (FFT) convolution in which the kernel is either a Gaussian or a cosine modulated Gaussian. Pedagogical examples of low-pass and band-pass filtering are provided, and the practical value of the spreadsheet is illustrated with some cases involving an earthquake record generated by a folded pendulum seismometer.

physics.gen-ph↗

Folded Pendulum Measurements of Earth's Free Oscillations

The nearly-incessant free oscillations of the Earth (not the larger, long-lived normal modes seen following intense quakes) were first observed by accident in the record of a tilt-sensitive instrument designed to study surface physics. Later tiltmeter studies demonstrated the usefulness of autocorrelation for the routine study of these normally short-lived eigenmodes. More recent studies suggest that many tilt-sensitive instruments are capable of observing these oscillations--if the low-frequency response of their electronics is not suppressed, as is customary with conventional designs.

physics.geo-ph↗

Friction as Basis for a Phonon Maser

Evidence is provided from experiment, for the hypothesis that defect organization (internal friction) is a means for operation of a phonon maser.

physics.gen-ph↗

Harmonic Oscillator Potential to describe Internal Dissipation

Assuming that a constant potential energy function has meaning for a dissipated harmonic oscillator, then an important issue is the time dependence of the turning points. Turning point studies demonstrate that the common model of external (viscous) damping fails to properly describe those many systems where structural (internal friction) damping is the most important source of dissipation. For internal friction damping, the better model of potential energy is one in which the function is not stationary.

physics.class-ph↗

Intuitive Derivation of Reynolds Number

It is evident from the literature that many engineers describe the Reynolds number qualitatively as ``the ratio of inertial forces to viscous forces''. Yet it is not immediately obvious that the well known expression Re = LV(rho)/(eta), which involves the size L of a solid object moving with speed V relative to a fluid of density rho and viscosity eta--is in fact a ratio of forces. It is hoped that the following treatment, which is based on an energy rather than force perspective, will help to de-mystify the important parameter given to us by Osborne Reynolds

physics.class-ph↗

The Flex-Pendulum -- Basis for an Improved Timepiece

A compound pendulum of simple geometry was built from a lightweight rod to which a pair of masses are clamped, one above and the other below the axis of rotation. By making the position of the upper mass variable, it was found that the characteristics of this pendulum can be altered dramatically. A theoretical model of the instrument is presented, which is in reasonable agreement with experimental observations. From the model it is shown that isochronism of the flex-pendulum can be significantly greater than that of the simple pendulum

physics.ed-ph↗

Nonlinear Damping of the 'Linear' Pendulum

This study shows that typical pendulum dynamics is far from the simple equation of motion presented in textbooks. A reasonably complete damping model must use nonlinear terms in addition to the common linear viscous expression. In some cases a nonlinear substitute for assumed linear damping may be more appropriate. Even for exceptional cases where all nonlinearity may be ignored, it is shown that viscous dissipation involves subtleties that can lead to huge errors when ignored.

physics.class-ph↗

Constant-Force-Magnitude Chaotic Oscillator

A numerical model is presented for a mechanical oscillator in which the magnitude of the restoring force is constant. Unlike the harmonic oscillator, where force is proportional to displacement, this nonlinear system can be chaotic when externally driven.

physics.gen-ph↗

Graphical explanation for the speed of the Fast Fourier Transform

For a sample set of 1024 values, the FFT is 102.4 times faster than the discrete Fourier transform (DFT). The basis for this remarkable speed advantage is the `bit-reversal' scheme of the Cooley-Tukey algorithm. Eliminating the burden of `degeneracy' by this means is readily understood using vector graphics.

math.HO↗

Anisotropic Internal Friction Damping

The mechanical damping properties of sheet polaroid material have been studied with a physical pendulum. The polaroid samples were placed under the knife-edges of the pendulum, which was operated in free-decay at a period in the vicinity of 10 s. With the edges oriented parallel to the direction of the long molecular chains in the polaroid, it was found that the damping was more than 10% smaller than when oriented perpendicular to the chains.

physics.class-ph↗

Oscillator damping with more than one mechanism of internal friction dissipation

The author's modified Coulomb damping model has been generalized to accommodate internal friction that derives from several dissipation mechanisms acting simultaneously. Because of its fundamental nonlinear nature, internal friction damping causes the quality factor Q of an oscillator in free-decay to change in time. Examples are given which demonstrate reasonable agreement between theory and experiment.

physics.class-ph↗