= Conservative forcing in averaged oscillator equations
{title2=$R_T=0,\quad \theta_T=-\langle f(R\cos\phi)\cos\phi\rangle/R$}
For a weak force depending only on <position>, the amplitude average is a periodic total <derivative> and vanishes. The leading harmonic amplitude is constant, while the phase may drift. The <method of multiple scales> agrees with the exact <conservation of energy> for bounded orbits in the effective potential. A cubic <position> force on the right side of the oscillator equation lowers the <frequency> at first order when its coefficient is positive.
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