= Second-order resonance from quadratic oscillator coupling
{title2=$T_2=\epsilon^2t$}
Two fundamental harmonics of <frequency> one multiply into only a constant and second harmonics. The first-order <solvability condition in the method of multiple scales> therefore has no amplitude-changing resonant coupling. Their first-order particular corrections can mix back into the fundamental at second order, selecting the possible scale $t=O(\epsilon^{-2})$. Detuning may suppress the resulting <resonance>, so identifying this scale alone does not prove instability for every initial state.
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