Related papers: Normal Mode Expansion of Damped Coupled Oscillator…
The problem of damping a system of linear oscillators is considered. The problem is solved by using a control in the form of dry friction. The motion of the system under the control is governed by a system of differential equations with…
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…
A modification of Coulomb's law of friction uses a variable coefficient of friction that depends on a power law in the energy of mechanical oscillation. Through the use of three different exponents: 0, 1/2 and 1; all commonly encountered…
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…
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…
We consider a standard optomechanical system where a mechanical oscillator is coupled to a cavity mode through the radiation pressure interaction. The oscillator is coherently driven at its resonance frequency, whereas the cavity mode is…
We study the dynamics of the entanglement between two oscillators that are initially prepared in a general two-mode Gaussian state and evolve while coupled to the same environment. In a previous paper we showed that there are three…
We consider a two-body quantum system in dimension one composed by a test particle interacting with an harmonic oscillator placed at the position $a>0$. At time zero the test particle is concentrated around the position $R_0$ with average…
Many natural and manmade dynamical systems that are modeled as large nonlinear multi-oscillator systems like power systems are hard to analyze. For such a system, we propose a nonlinear modal decoupling (NMD) approach inversely constructing…
In the frame of the Lindblad theory of open quantum systems, the system of three uncoupled harmonic oscillators with opening operators linear in the coordinates and momenta of the considered system is analyzed. The damping of the angular…
This article deals with a nonrelativistic quantum mechanical study of a dynamical system which generalizes the isotropic harmonic oscillator system in three dimensions. The problem of interbasis expansions of the wavefunctions is completely…
The question of decoupling and freeze-out is reinvestigated and analysed in terms of transparent semi-classical decoupling formulae, which provide a smooth decoupling in time both, for single and two particle inclusive spectra. They…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
The influence of gapless dissipative degrees of freedom on the superconductor-insulator transition in two dimensions is investigated. We develop a series expansion for the free energy of a (2+1)-dimensional XY model coupled to a bosonic…
The objective of the present study is to explore the connection between the nonlinear normal modes of an undamped and unforced nonlinear system and the isolated resonance curves that may appear in the damped response of the forced system.…
Through a set of generators that preserves the hermiticity and trace of density matrices, we analyze the damping of harmonic oscillator in open quantum systems into four modes, distinguished by their specific effects on the covariance…
It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model…
We studied equally charged particles, suspended in a complex plasma, which move in a plane and interact with a screened Coulomb potential (Yukawa type) and with an additional external confining parabolic potential in one direction, that…
We investigate an oscillator linearly coupled with a one-dimensional Ising system. The coupling gives rise to drastic changes both in the oscillator statics and dynamics. Firstly, there appears a second order phase transition, with the…
Quantum mechanics of a general one dimensional dissipative system investigated by it's coupling to a Klein-Gordon field as the environment using a minimal coupling method. Heisenberg equation for such a dissipative system containing a…