Oscillation time and damping coefficients in a nonlinear pendulum

TL;DR

This paper explores how damping affects the oscillation time in a nonlinear pendulum, revealing conditions where the oscillation period varies non-monotonically with damping.

Contribution

It establishes a relationship between damping coefficients and oscillation time, and identifies conditions causing non-monotonic dependence in nonlinear pendulums.

Findings

Oscillation time can vary non-monotonically with damping.

Conditions on the nonlinear force influence oscillation period.

Relationship between damping and oscillation time is characterized.

Abstract

We establish a relationship between the normalized damping coefficients and the time that takes a nonlinear pendulum to complete one oscillation starting from an initial position with vanishing velocity. We establish some conditions on the nonlinear restitution force so that this oscillation time does not depend monotonically on the viscosity damping coefficient.