Exact and approximate expressions for the period of anharmonic oscillators

TL;DR

This paper introduces a systematic method for calculating the period of anharmonic oscillators, providing both exact and approximate solutions to integrals common in classical mechanics.

Contribution

The paper presents a new systematic approach for evaluating integrals related to anharmonic oscillator periods, enhancing accuracy and efficiency.

Findings

Derived exact expressions for oscillator periods.

Developed approximate formulas with high accuracy.

Applicable to a range of anharmonic potentials.

Abstract

In this paper we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulas for the period of anharmonic oscillators and other problems of interest in classical mechanics.