(a) A box of mass m, attached to a spring, oscillates in simple harmonic motion on a frictionless surface as indicated in the figure below. Each time the box reaches the point of maximum displacement a child allows some sand to fall vertically into the box. This will gradually increase the mass of the system. Briefly explain what will happen to the period of oscillation as sand is added. ￼￼￼(b) A spring hangs vertically from a ceiling with a mass m = 3.0 kg attached to its lower end. The spring constant is k = 45 N.m-1. Initially, you hold the mass in your hand so that the spring is at its natural length (neither stretched nor compressed). At t = 0 s you release the mass from rest. (i) Find a value for the period of oscillation of this spring-mass system. (ii) Find a value for the amplitude.