Odd position-dependent damping has zero first-order amplitude drift

If $f$ is odd, its average $⟨f(A\cos \psi ){\sin }^2\psi ⟩$ 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.