Details

Autor(en) / Beteiligte

• Salas, Alvaro H.
• Mosquera P, Darin J.
• Castillo H., Jairo E.
• Clementi, Francesco
• Francesco Clementi

Titel

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

Ist Teil von

• Mathematical problems in engineering, 2020, Vol.2020 (2020), p.1-7

Ort / Verlag

Cairo, Egypt: Hindawi Publishing Corporation

Erscheinungsjahr

2020

Quelle

Free E-Journal (出版社公開部分のみ）

Beschreibungen/Notizen

• 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.