Exponential versus linear amplitude decay in damped oscillators

We analyze a simple textbook approach to nonlinear oscillators proposed recently, disclose its errors, limitations and misconceptions and complete the calculations that the authors failed to perform.

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 sliding fiction in common harmonic oscillator equations, allowing to separate these different types of dissipation. To compare this model with experimental data, a nanometric vibration was imposed on a quartz tuning fork, while an atomic force ...

This note is an addendum to the results of P.O. Frederickson and A.C. Lazer [1], and A.C. Lazer [4] on periodic oscillations, with linear part at resonance. We show that a small modification of the argument in [4] provides a more general result. It turns out that things are different for the corresponding Dirichlet boundary value problem.

In this paper the general solution of the quantum damped harmonic oscillator is given.

Theoretically, solutions of the damped harmonic oscillator asymptotically approach equilibrium, i.e., the zero energy state, without ever reaching it exactly, and the critically damped solution approaches equilibrium faster than the underdamped or the overdamped solution. Experimentally, the systems described with this model reach equilibrium when the system's energy has dropped below some threshold corresponding to the energy resolution of the measuring apparatus. We show th...

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.

In this study, we examine the asymptotic behavior of solutions to nonlinear Schr\"{o}dinger equations with time-dependent harmonic oscillators and prove the time-decay property of solutions in the case of a long range power type nonlinearity.

Hereditary effects of exponentially damped oscillators with past histories are considered in this paper. Nonviscously damped oscillators involve hereditary damping forces which depend on time-histories of vibrating motions via convolution integrals over exponentially decaying functions. As a result, this kind of oscillators are said to have memory. In this work, initialization for nonviscously damped oscillators is firstly proposed. Unlike the classical viscously damped ones,...

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 C...

A condition which guaranties the exponential decay of the solutions of the initial-boundary value problem for the damped wave equation is proved. A method for the effective computability of the coefficient of exponential decay is also presented.