Resonance oscillation of a damped driven simple pendulum

TL;DR

This paper numerically investigates the resonance behavior of a driven damped simple pendulum, highlighting differences from harmonic oscillators and providing insights into its nonchaotic dynamics for educational purposes.

Contribution

It reports the resonance characteristics of a driven damped pendulum through numerical analysis, a topic not previously explored due to analytical challenges.

Findings

Resonance features differ from harmonic oscillators.

Numerical results reveal rich nonchaotic dynamics.

Comparison with harmonic oscillator resonance characteristics.

Abstract

The resonance characteristics of a driven damped harmonic oscillator are well known. Unlike harmonic oscillators which are guided by parabolic potentials, a simple pendulum oscillates under sinusoidal potentials. The problem of an undamped pendulum has been investigated to a great extent. However, the resonance characteristics of a driven damped pendulum have not been re- ported so far due to the difficulty in solving the problem analytically. In the present work we report the resonance characteristics of a driven damped pendulum calculated numerically. The results are compared with the resonance characteristics of a damped driven harmonic oscillator. The work can be of pedagogic interest too as it reveals the richness of driven damped motion of a simple pendulum in comparison to and how strikingly it differs from the motion of a driven damped harmonic oscillator. We confine our work only to the nonchaotic regime of pendulum motion.