= Zero-canonical-angular-momentum ring oscillation
{title2=$\Omega^2=4\pi^2k/m+q^2B^2/(4m^2)$}
With $J=0$, define $\omega_s^2=4\pi^2k/m$ and $\omega_c=qB/m$. Then $r_e=\omega_s^2r_0/(\omega_s^2+\omega_c^2/4)$, the radial frequency is $\Omega=\sqrt{\omega_s^2+\omega_c^2/4}$, and release at $r_0$ gives $r=r_e+(r_0-r_e)\cos\Omega t$ with $\dot\phi=-\omega_c/2$. The physical solution requires $r>0$. If $2r_e<r_0$, the formal oscillation reaches zero and cannot be continued as a negative ring radius without a new collapse model.
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