In this paper, He’s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy. Keywords—He’s amplitude frequency formulation; Periodic solution; Nonlinear oscillator; Fractional potential.

We show that nonlinear response of a quantum oscillator displays antiresonant dips as the field frequency passes adiabatically through multiphoton resonance. This coherent quantum effect has no analog in two-level systems. Its emergence is a consequence of special symmetry of a weakly nonlinear oscillator. We discuss the possibility to observe the antiresonance and the associated multiphoton Ra...

An oscillator whose frequency is amplitude dependent can be controlled by a drive whose frequency sweeps through a resonance with the oscillator's fundamental frequency. This phenomenon is called autoresonance, and has been previously investigated for drives with frequencies near the oscillator's fundamental or subharmonic frequencies. This paper examines autoresonance for drives at twice the f...

The amplitude–frequency relationship is an important mathematical property for a nonlinear oscillator. He’s amplitude–frequency formulation and the Max–Min approach are used to handle the conservative nonlinear oscillator ẍ +  1 + ẋ2  x = 0 for the amplitude–frequency relationship. The obtained result is compared with those in the open literature, revealing the effectiveness of the used metho...

We study the resonant dynamics of a two-degree-of-freedom system composed a linear oscillator weakly coupled to a strongly nonlinear one, with an essential (nonlinearizable) cubic stiffness nonlinearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show...

We consider the Bose–Einstein condensate in a parabolic trap as a macroscopic quantum oscillator and describe, analytically and numerically, its collective modes — a nonlinear generalisation of the (symmetric and antisymmetric) Hermite–Gauss eigenmodes of a harmonic quantum oscillator.  2001 Elsevier Science B.V. All rights reserved. PACS: 03.75.F; 03.75.-b; 03.50.-z; 73.20.Dx The recent obser...

The scattering of ultrasound from bubbles of ∼ 1 μm radius, such as used in contrast enhancers for ultrasound diagnostics, is studied. We show that sound scattering and “active” emission of sound from oscillating bubbles are not contradictory, but are just two different aspects derived from the same physics. Treating the bubble as a nonlinear oscillator, we arrive at general formulas for scatte...

the current paper focuses on some analytical techniques to solve the non-linear duffing oscillator with large nonlinearity. four different methods have been applied for solution of the equation of motion; the variational iteration method, he’s parameter expanding method, parameterized perturbation method, and the homotopy perturbation method. the results reveal that approximation obtained by th...

in this study, a new efficient semi-analytical method is introduced to give approximate solutions of strongly nonlinear oscillators. the proposed method is based on combination of two different methods, the multi-step homotopy analysis method and spectral method, called the multi-step spectral homotopy analysis method (msham). in this method, firstly, we propose a new spectral homotopy analysis...