Related papers: Exponential versus linear amplitude decay in dampe…
We show how to adapt the approach introduced for viscous damping in [1] to derive the approximate amplitude decay in the case of damping by a force of constant magnitude (sliding friction) and in the case of damping by a force proportional…
We derive approximate expressions for the amplitude decay of harmonic oscillations weakly damped by the simultaneous action of three different damping forces: force of constant magnitude, force linear in velocity, and force quadratic in…
We demonstrate how to derive the exponential decrease of amplitude and an excellent approximation of the energy decay of a weakly damped harmonic oscillator without solving the associated equation of motion and without insight into the…
Applying a technique developed in a recent work[1] to calculate wavefunction evolution in a dissipative system with Ohmic friction, we show that the wavelength of the wavefunction decays exponentially, while the Brownian motion width…
We consider an abstract linear wave equation with a time-dependent dissipation that decays at infinity with the so-called scale invariant rate, which represents the critical case. We do not assume that the coefficient of the dissipation…
A pedagogically instructive experimental procedure is suggested for distinguishing between different damping terms in a weakly damped oscillator, which highclights the connection between non-linear damping and initial-amplitude dependence.…
Sliding friction is ubiquitous in nature as are harmonic oscillators. However, when treating harmonic oscillators the effect of sliding friction is often neglected. Here, we propose a simple analytical model to include both viscous and…
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…
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…
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…
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate…
We study the nonlinear behaviors of mass-spring systems damped by dry friction using simulation by a nonlinear LC circuit damped by anti-parallel diodes. We show that the differential equation for the electric oscillator is equivalent to…
Two manifestations of decoherence, called instantaneous and dynamical, are investigated. The former reflects the suppression of the interference between the components of the current state while the latter reflects that within the initial…
An approximate solution is presented for simple harmonic motion in the presence of damping by a force which is a general power-law function of the velocity. The approximation is shown to be quite robust, allowing for a simple way to…
We introduce a new approach to deriving approximate analytical solutions of a harmonic oscillator damped by purely nonlinear, or combinations of linear and nonlinear damping forces. Our approach is based on choosing a suitable trial…
If a contact of two purely elastic bodies with no sliding (infinite coefficient of friction) is subjected to superimposed oscillations in the normal and tangential directions, then a specific damping appears, that is not dependent on…
The dynamics of a pair of coupled harmonic oscillators in separate or common thermal environments is studied, focusing on different indicators of quantumness, such as entanglement, twin oscillators correlations and quantum discord. We…
We investigate a simple forced harmonic oscillator with a natural frequency varying with time. It is shown that the time evolution of such a system can be written in a simplified form with Fresnel integrals, as long as the variation of the…
We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical…
Time-decaying harmonic oscillators yield dispersive estimates with weak decay, and change the threshold power of the nonlinearity between the short and the long range. In the non-critical case for the time-decaying harmonic oscillator, this…