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Light damping leaves the oscillation sinusoidal but shrinks its envelope exponentially, A(t) = A0 exp(-bt/2m). With b = 0.8 kg/s on a 2 kg mass the decay constant is 0.2 per second, so amplitude halves every 3.47 s and after 3 s only 55% remains. Energy falls twice as fast as amplitude because it goes with the square.
Amplitude envelope
A(t) = A0 x exp(-b t / 2m)
Amplitude half-life
t(half) = ln2 x 2m / b
The value of b that just prevents oscillation, b = 2 sqrt(km). Below it the system rings; above it the return is sluggish.
Because energy is proportional to amplitude squared, so its decay constant is twice as large.