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Theoretically, solutions of the damped harmonic oscillator asymptoticallyapproach equilibrium, i.e., the zero energy state, without ever reaching itexactly, and the critically damped solution approaches equilibrium faster thanthe underdamped or the overdamped solution. Experimentally, the systemsdescribed with this model reach equilibrium when the system's energy hasdropped below some threshold corresponding to the energy resolution of themeasuring apparatus. We show that one can (almost) always find an optimalunderdamped solution that will reach this energy threshold sooner than allother underdamped solutions, as well as the critically damped solution, nomatter how small this threshold is. We also comment on one exception to thisfor a particular type of initial conditions, when a specific overdampedsolution reaches the equilibrium state sooner than all other solutions. Weconfirm some of our findings experimentally.

Damped harmonic oscillator revisited: the fastest route to equilibrium