English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The Fourier-based analysis customarily employed to analyze the dynamics of asimple pendulum is here revisited to propose an elementary iterative schemeaimed at generating a sequence of analytical approximants of the exact law ofmotion. Each approximant is expressed by a Fourier sum whose coefficients aregiven by suitable linear combinations of Bessel functions, which are expectedto be more accessible, especially at an undergraduate level, with respect toJacobian elliptic functions. The first three approximants are explicitelyobtained and compared with the exact solution for typical initial angularpositions of the pendulum. In particular, it is shown that, at the lowestapproximation level, the law of motion of the pendulum turns out to beadequately described, up to oscillation amplitudes of $\pi/2$, by a sinusoidaltemporal behaviour with a frequency proportional to the square root of theso-called "besinc" function, well known in physical optics.

Simple pendulum dynamics: revisiting the Fourier-based approach to the solution