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Damped harmonic oscillator revisited: The fastest route to equilibrium

Lelas, Karlo ; Poljak, Nikola ; Jukić, Dario

American journal of physics, 2023-10, Vol.91 (10), p.767-775 [Periódico revisado por pares]

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Título:
Damped harmonic oscillator revisited: The fastest route to equilibrium
Autor: Lelas, Karlo ; Poljak, Nikola ; Jukić, Dario
É parte de: American journal of physics, 2023-10, Vol.91 (10), p.767-775
Descrição: Theoretically, solutions of the damped harmonic oscillator asymptotically approach equilibrium, i.e., the zero energy state, without ever reaching it exactly, and the critically damped solution approaches equilibrium faster than the underdamped or the overdamped solution. Experimentally, the systems described with this model reach equilibrium when the system's energy has dropped below some threshold corresponding to the energy resolution of the measuring apparatus. We show that one can (almost) always find an optimal underdamped solution that will reach this energy threshold sooner than all other underdamped solutions, as well as the critically damped solution, no matter how small this threshold is. We also comment on one exception to this for a particular type of initial condition, when a specific overdamped solution reaches the equilibrium state sooner than all other solutions. We experimentally confirm some of our findings.
Editor: Woodbury: American Institute of Physics
Idioma: Inglês

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