Driven damped harmonic oscillator revisited: energy resonance

TL;DR

This paper derives an exact expression for the energy resonance frequency of a driven damped harmonic oscillator and shows it closely relates to amplitude resonance, providing insights into energy behavior at resonance.

Contribution

It introduces an exact formula for the energy resonance frequency and links it to amplitude resonance, enhancing understanding of energy dynamics in oscillators.

Findings

Energy resonance frequency is accurately approximated by the mean of amplitude and velocity resonant frequencies.

Amplitude resonance frequency corresponds to the peak of instantaneous energy.

Derived expression improves the analysis of energy behavior in damped harmonic oscillators.

Abstract

We derive the exact expression for the resonant frequency of the time-averaged steady-state energy and show that this frequency is excellently approximated by the arithmetic mean of the amplitude and velocity resonant frequencies. In addition, we argue that the frequency of the amplitude resonance can be regarded as the energy resonance frequency, since it provides the maximal peak values of instantaneous energy.