A thin, rigid insulating ring of radius \(R\) lies in the \(xy\)-plane and carries a total positive charge \(Q\) distributed uniformly along its circumference. A particle of mass \(m\) and negative charge \(-q\) is constrained to move along the central \(z\)-axis perpendicular to the plane of the ring. The particle is released from rest at a small displacement \(z\) from the center of the ring, where \(z \ll R\). Which of the following expressions is the angular frequency \(\omega\) of the particle's small oscillations?