Translating harmonic trap on a circular orbit ($\ddot{\mathbf{q}}+{\omega }^2\mathbf{q}=R{\Omega }^2(\cos \Omega t,\sin \Omega t)$)

A nonrotating frame whose origin travels on a circle carries a spatially uniform fictitious force. A harmonic trap fixed to that origin therefore drives its relative coordinate by the displayed equation. Away from resonance its circular particular response has radius $R{\Omega }^2/({\omega }^2-{\Omega }^2)$. At ${\omega }^2={\Omega }^2\ne 0$, the response grows linearly in time. Rotating the coordinate axes adds Coriolis and centrifugal terms but does not change this physical resonance condition.