Two positive point charges +q are on the y axis at y = +a and y = –a as in Problem 32. A bead of mass m carrying a negative charge –q slides without friction along a thread that runs along the x axis

(a) Show that for small displacements of x << a, the bead experiences a restoring force that is proportional to x and therefore undergoes simple harmonic motion.

(b) Find the period of the motion.