A particle of mass m is placed on a frictionless horizontal table and attached by two identical massless spicral springs of natural length b and stiffness k, to two fixed points A and B on the table. Points A and B are a distance 2a apart, where 2a>2b, so that the springs are stretched. The particle is then given a displacement along the line of the springs and released. Show that the motion that ensues is simple harmonic motion, and find its period.