A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications
Joint Authors
Salas, Alvaro H.
Castillo H., Jairo E.
Mosquera P, Darin J.
Source
Mathematical Problems in Engineering
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-7, 7 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-10-07
Country of Publication
Egypt
No. of Pages
7
Main Subjects
Abstract EN
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″=Fz in the sense that z=zt.
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.
American Psychological Association (APA)
Salas, Alvaro H.& Castillo H., Jairo E.& Mosquera P, Darin J.. 2020. A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications. Mathematical Problems in Engineering،Vol. 2020, no. 2020, pp.1-7.
https://search.emarefa.net/detail/BIM-1200748
Modern Language Association (MLA)
Salas, Alvaro H.…[et al.]. A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications. Mathematical Problems in Engineering No. 2020 (2020), pp.1-7.
https://search.emarefa.net/detail/BIM-1200748
American Medical Association (AMA)
Salas, Alvaro H.& Castillo H., Jairo E.& Mosquera P, Darin J.. A New Approach for Solving the Undamped Helmholtz Oscillator for the Given Arbitrary Initial Conditions and Its Physical Applications. Mathematical Problems in Engineering. 2020. Vol. 2020, no. 2020, pp.1-7.
https://search.emarefa.net/detail/BIM-1200748
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1200748