A small bead of mass $m$ is held at the origin by two identical ideal springs, each of stiffness $k$ and natural length $\ell_0$. The springs are anchored to walls at $(+L, 0, 0)$ and $(-L, 0, 0)$ with $L > \ell_0$, so each spring is stretched at equilibrium. Gravity is negligible. The entire apparatus (walls, springs, and bead) is then rotated rigidly about the $x$-axis at constant angular velocity $\omega$. For what range of $\omega$ is the equilibrium at the origin stable to small displacements perpendicular to the rotation axis?