Vertical oscillation — UPSC Physics Optional IFoS 2011 Paper I

A light spring of relaxed length 'a_0' is suspended from a point. It carries a mass 'm' at its lower free end, which stretches it through a distance l. Show that the vertical oscillation of the system is simple harmonic in nature and has time period T = 2\pi \sqrt{l / g}, where g is the acceleration due to gravity.