= Velocity-only forcing in averaged oscillator equations
{title2=$\theta_T=0,\quad R_T=-\langle f(-R\sin\phi)\sin\phi\rangle$}
When the weak force depends only on <velocity>, the phase average is a periodic total <derivative> and vanishes. The leading phase is constant, while the amplitude evolves according to the remaining average. The sign of that drift determines damping or growth and must be checked from the force, rather than inferred from its <velocity> dependence alone.
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