Relaxation time in damped harmonic oscillators is defined as the duration required for mechanical energy to decay to 1/e of its initial value. This specific ratio of 1/e is significant as it represents the natural time scale of the system. The amplitude of a damped harmonic oscillator decreases over time according to the equation e-t/τ, where τ denotes the relaxation time. This time scale is crucial as it differentiates between the oscillatory behavior of the system when t << τ and the fully damped state when t >> τ.
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