One More Tool for Understanding Resonance

TL;DR

This paper introduces a time-domain graphical convolution method to analyze resonance, capturing both transient and steady-state oscillations, and offers a new perspective on resonance based on waveform analysis rather than frequency domain.

Contribution

It presents a novel application of graphical convolution for resonance analysis, emphasizing time-domain interpretation and non-sinusoidal waveforms, expanding traditional frequency-based approaches.

Findings

Provides a unified analysis of transient and steady-state resonance.

Introduces a new time-domain definition of resonance.

Connects waveform analysis with Fourier series concepts.

Abstract

We propose the application of graphical convolution to the analysis of the resonance phenomenon. This time-domain approach encompasses both the finally attained periodic oscillations and the initial transient period. It also provides interesting discussion concerning the analysis of non-sinusoidal waves, based not on frequency analysis, but on direct consideration of waveforms, and thus presenting an introduction to Fourier series. Further developing the point of view of graphical convolution, we come to a new definition of resonance in terms of time domain.