Comments on ‘A finite extensibility nonlinear oscillator’

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Comments 
 on 
 ‘ A 
 finite 
 extensibility 
 nonlinear 
 oscillator ’ 
 Applied 
 Mathematics 


The aim of this comment is to extend the study of the dynamics of a finite extensibility nonlinear oscillator conducted by Febbo [M. Febbo, A finite extensibility nonlinear oscillator, Applied Mathematics and Computation 217 (2011) 6464-6475]. We show that the linearized harmonic balance method is not sufficiently adequate for this oscillator and that the harmonic balance method without lineari...

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Unlike its classical counterpart, the ground state of a quantum harmonic oscillator yields a non-zero value which has led to a significant problem regarding the cosmological constant. We will show that since observables, including that of energy, serve as a reference frame for an observer, not only is the harmonic oscillator fluctuating at the ground level, so is the reference frame of the obse...

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Notes on a conservative nonlinear oscillator

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...

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Noise-induced Effects on a Nonlinear Oscillator

We examine various phenomena induced by white Gaussian random perturbations in the response of nonlinear dynamical systems. In the rst part of this work, digital and analog experiments are conducted on a simple single-degree-of-freedom oscillator with piecewise linear restoring force and harmonic forcing. They reveal that small noise perturbations can give rise to large deviations of the respon...

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ژورنال

عنوان ژورنال: Applied Mathematics and Computation

سال: 2012

ISSN: 0096-3003

DOI: 10.1016/j.amc.2011.12.012