A trolley of mass m is fixed to the end of a spring. The spring can be compressed and extended. The spring has a force constant k. The other end of the spring is attached to a vertical wall. The trolley lies on a smooth horizontal table. The trolley oscillates when it is displaced from its equilibrium position.

a. Show that the motion of the oscillating trolley is s.h.m.
b. Show that the period T of the trolley is given by the equation:

T = 2π √m/k