A simple energy-dissipation argument gives approximate linear and inverse-time amplitude decay for harmonic oscillators with sliding friction and velocity-squared air resistance.
An elementary proof of the amplitude’s exponential decrease in damped oscillations
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Addendum: Modeling the amplitude and energy decay of a weakly damped harmonic oscillator using the energy dissipation rate and a simple trick (2025 Eur. J. Phys. 46(1) 015004)
A simple energy-dissipation argument gives approximate linear and inverse-time amplitude decay for harmonic oscillators with sliding friction and velocity-squared air resistance.