Four equal charges, q, are fixed at the corners of a square of side a in the xy-plane centered on the origin. A bead of mass m and charge -q is positioned at the origin. A thin, frictionless string along the z-axis threads the bead, thus restricting its mo- tion to the z-axis. The bead is then displaced from the origin by a small amount Zo < 0 and released from rest. Show that the bead undergoes simple harmonic motion (to a very good approximation), and derive an expression for its period of oscillation in terms of known parameters.

Four equal charges, q, are fixed at the corners of a square of side a in the xy-plane centered on the origin. A bead of mass m and charge -q is positioned at the origin. A thin, frictionless string along the z-axis threads the bead, thus restricting its mo- tion to the z-axis. The bead is then displaced from the origin by a small amount Zo < 0 and released from rest. Show that the bead undergoes simple harmonic motion (to a very good approximation), and derive an expression for its period of oscillation in terms of known parameters.