The main objective of the present work is to find an approximate analytical solution for nonlinear differential equation vibro-impact oscillator under influence electromagnetic actuation near primary resonance. trigger regime due Hertzian contact. optimal auxiliary functions method (OAFM) utilized give problem. influences static normal load and resonance are completely studied. novelties propos...

By taking a Klein-Gordon field as the environment of an harmonic oscillator and using a new method for dealing with quantum dissipative systems (minimal coupling method), the quantum dynamics and radiation reaction for a quantum damped harmonic oscillator investigated. Applying perturbation method, some transition probabilities indicating the way energy flows between oscillator, reservoir and q...

In this paper we revisit the quantum damped harmonic oscillator and construct an interesting approximate solution in the operator algebra level. Namely, we first give the general solution to the Lindblad form (equation) and next construct an approximate solution to the full equation by use of it. Our method is a milestone to construct the general solution. In this paper we revisit dynamics of a...

We consider the Fermi quantization of the classical damped harmonic oscillator (dho). In past work on the subject, authors double the phase space of the dho in order to close the system at each moment in time. For an infinite-dimensional phase space, this method requires one to construct a representation of the CAR algebra for each time. We show that unitary dilation of the contraction semigrou...

This paper describes the physical relationships that exist between the Fourier transform and the response spectrum of a strong-motion accelerogram. By developing the new concept of the "Damped Fourier Spectrum" (D.F.S.), we show that the velocity and displacement of the damped oscillator can be represented by a linear combination of the real and imaginary parts of the D.F.S. and by the initial ...

We study the nonlinear oscillations of a forced and weakly dissipative spring– magnet system moving in the magnetic fields of two fixed coaxial, hollow induction coils. As the first coil is excited with a dc current, both a linear and a cubic magnet-position dependent force appear on the magnet–spring system. The second coil, located below the first, excited with an ac current, provides the osc...

the dynamical behaviour of the forced escape oscillator, which depends on the parameter values we considered, have been studied numerically using the techniques of phase portraits and poincar'{e} sections. also, we employed perturbation methods such as lindstedt's method to obtain the frequency-amplitude relation of escape oscillator.