Experimental and Theoretical Physics Studies
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Abstract
Abstract
Abstract In this work, we consider a damped harmonic oscillator submitted to an applied force which has a harmonic time dependence and show that there is a third resonance that is not discussed in the literature. In fact, the frequency of the applied force that maximizes the average energy of the harmonic oscillator (HO) in the stationary regime does not coincide with its natural frequency nor with the frequency that maximizes its amplitude. We compute this third resonance frequency explicitly and verify that it lies between the other two resonance frequencies. Physical interpretations are provided for this (apparent) unexpected result. Finally, we compare the maximum value of the average energy of the HO (evaluated at this new resonance frequency) with its value evaluated at the resonance frequency of the power of the applied force and show that the former can be substantially greater than the latter for high enough values of the damping factor.
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@article{Moura2026third,
title = {A third resonance in the damped and forced harmonic oscillator},
author = {Matheus Moura and Reinaldo de Melo e Souza and Carlos Farina},
journal = {European Journal of Physics},
year = {2026},
doi = {10.1088/1361-6404/ae7bd3},
url = {https://doi.org/10.1088/1361-6404/ae7bd3}
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