Experiment on impulsive excitation, resonance, and Fourier analysis of a harmonic oscillator

Abstract

It is shown how a simple electrical circuit may be made to operate as an impulsively excited damped harmonic oscillator having independently variable natural frequency and damping. The oscillator’s response is developed in a particularly transparent way through impulse analysis, a technique that is wholly within the time domain and provides an alternative to Fourier analysis in the frequency domain. Resonance is exhibited and interpreted using impulse analysis, and through resonance, contact is made with Fourier analysis.

Some applications of Fourier's great discovery for beginners

“…For those, the period is accepted to be infinity, and the summation is replaced by integration. Fourier analysis constitutes an important part of laboratory courses [2][3][4][5][6][7][8][9][10][11][12][13]. Higgins [2] presented an introduction to this technique.…”

“…Higgins [2] presented an introduction to this technique. It is very natural to use an LC resonant circuit for separating the harmonics [3][4][5]. Sandoval and Porta [6] presented an analysis of the vibration of a string using optical detection.…”