= Radial spring oscillator on a rotating guide
{title2=$\omega_{\rm osc}^2=k/m-\Omega^2$}
A <point mass> constrained to a straight guide through the axis of a uniformly <rotating reference frame>, with signed central displacement $x$ and <Hooke's law> <force> $-kx$, satisfies $m\ddot x=-kx+m\Omega^2x$. The transverse <Coriolis force> is balanced by the guide. The central <equilibrium> is stable for $\Omega^2<k/m$ and unstable above it. At equality the restoring coefficient vanishes and $x(t)=x_0+v_0t$: a small initial <velocity> causes unbounded drift in the ideal guide. The threshold therefore has no positive oscillation frequency. The <angular frequency> is the positive square root in the title.
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