A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications

Author:

Salas S Alvaro H.1ORCID,Castillo H Jairo E.2,Mosquera P Darin J.3

Affiliation:

1. Universidad Nacional de Colombia, Department of Mathematics and Statistics, FIZMAKO Research Group, Bogota, Colombia

2. Universidad Distrital Francisco José de Caldas, FIZMAKO Research Group, Bogota, Colombia

3. Universidad Distrital Francisco José de Caldas, ORION Research Group, Bogota, Colombia

Abstract

In this paper, a new analytical solution to the undamped Helmholtz oscillator equation in terms of the Weierstrass elliptic function is reported. The solution is given for any arbitrary initial conditions. A comparison between our new solution and the numerical approximate solution using the Range Kutta approach is performed. We think that the methodology employed here may be useful in the study of several nonlinear problems described by a differential equation of the form z = F z in the sense that z = z t . In this context, our solutions are applied to some physical applications such as the signal that can propagate in the LC series circuits. Also, these solutions were used to describe and investigate some oscillations in plasma physics such as oscillations in electronegative plasma with Maxwellian electrons and negative ions.

Funder

University Francisco Jose de Caldas

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

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