= Supremum of two incommensurate harmonic modes
{title2=$\sup_t|x(t)|=|A|+|B|$}
For $x(t)=A\cos\omega_1t+B\cos\omega_2t$ with irrational <frequency> ratio and nonzero <amplitudes>, $|x|\le|A|+|B|$. The <phase> trajectory is dense on the two-torus, so this bound is a <supremum>. The required exact <phase> alignment may never occur at finite time. Thus an exam's maximum-amplitude estimate can be a limiting bound rather than an attained displacement; finite observation intervals have smaller maxima.
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