On the approximate solutions to a damped harmonic oscillator with higher-order nonlinearities on a rough plane

Jiaxing Li

doi:10.1117/12.2672681

28 March 2023 On the approximate solutions to a damped harmonic oscillator with higher-order nonlinearities on a rough plane

Jiaxing Li

Author Affiliations +

Proceedings Volume 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022); 1259710 (2023) https://doi.org/10.1117/12.2672681
Event: Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 2022, Nanjing, China

Abstract

The harmonic oscillator is an important physical model in both classical mechanics and quantum mechanics which describes the dynamics of an object displaced from its equilibrium position. The damped harmonic oscillator has already been well studied on a smooth plane. However, it is hard to avoid energy dissipation caused by a plane in real cases. Hence, in this paper, the approximate solutions to a damped harmonic oscillator with higher-order nonlinearities on a rough plane is explored mainly by the Cardano-Tartaglia formula. In approximate solutions, an approximate solution is provided under specific prerequisite and a case is studied given the initial conditions. Also, the system error of the approximate solution in approximate solutions is analyzed in error analysis under the restrictions of the initial conditions. In this paper, only a short time span of the damped harmonic oscillator dynamics is analyzed because of the existence of two terms which are mentioned in error analysis.

Citation Download Citation

Jiaxing Li "On the approximate solutions to a damped harmonic oscillator with higher-order nonlinearities on a rough plane", Proc. SPIE 12597, Second International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2022), 1259710 (28 March 2023); https://doi.org/10.1117/12.2672681

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available