For a harmonic oscillator under combined sliding, linear, and quadratic damping, amplitude decay is described by a solvable first-order envelope equation whose solutions match numerical integration in the weak-damping limit.
Young and Roger A
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The amplitude decay of a harmonic oscillator damped simultaneously by weak linear and nonlinear damping forces
For a harmonic oscillator under combined sliding, linear, and quadratic damping, amplitude decay is described by a solvable first-order envelope equation whose solutions match numerical integration in the weak-damping limit.