In this paper, the efficient multi-step differential transform method (EMsDTM) is applied to get the accurate approximate solutions for strongly nonlinear duffing oscillator. The main improvement of EMsDTM which is to reduce the number of arithmetic operations, is thoroughly investigated and compared with the classic multi-step differential transform method (MsDTM). To illustrate the applicabil...

The linearly damped oscillator equation is considered with the damping term generalized to a Caputo fractional derivative. The order of the derivative being considered is 0 ≤ v ≤ 1. At the lower end v 0 the equation represents an undamped oscillator and at the upper end v 1 the ordinary linearly damped oscillator equation is recovered. A solution is found analytically, and a comparison with the...

here, we have considered the husimi and wigner distribution functions. we have, inparticular, shown how the uncertainty principle works for the two cases of simple and damped harmonicoscillators when either of these two distributions are used. the conclusion shows that the husimidistribution function remains non-negative through the phase space but it does not always satisfies theuncertainty pr...

In the present investigation, a quadratically forced damped pendulum-type equation is solved analytically using several effective and highly accurate approaches. Some different types of pendulum oscillators linked to terms, in addition power damping term, are analyzed. first part, Krylov–Bogoliubov–Mitropolsky (KBM) technique ansatz method carried out for analyzing oscillator. second two varian...

In this investigation, two different models for coupled asymmetrical oscillators, known as, forced damped Duffing oscillators (FDDOs) are reported. The first model of FDDOs consists a nonlinear oscillator (FDDO) with linear oscillator, while the second is composed FDDOs. Krylov–Bogoliubov–Mitropolsky (KBM) method, carried out analyzing any model. To do that, reduced to decoupled system individu...

We study the impulsive responses of a grounded linear oscillator coupled to a light nonlinear attachment through an essentially nonlinear (nonlinearizable) stiffness. We analyze the periodic and quasi-periodic dynamics of the undamped system forced by a single impulse on the linear oscillator and being initially at rest, by considering separately low-, moderateand high-energy impulsive motions....

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.

We show theoretically how a driven harmonic oscillator can be used as a quantum simulator for the non-Markovian damped harmonic oscillator. In the general framework, our results demonstrate the possibility to use a closed system as a simulator for open quantum systems. The quantum simulator is based on sets of controlled drives of the closed harmonic oscillator with appropriately tailored elect...