= Odd position-dependent damping has zero first-order amplitude drift
= Zero first-order amplitude drift for odd damping
{synonym}
If $f$ is odd, its average $\langle f(A\cos\psi)\sin^2\psi\rangle$ vanishes under a half-period shift. Hence the <averaged amplitude for position-dependent damping> is constant at first order. Odd-power damping creates only even harmonics when multiplied by the leading oscillator velocity; these do not resonate with the fundamental harmonic. Higher-order drift is still possible.
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