A small ball of mass 0.40kg is released from a point 0.60m above the top end of an unstretched vertical spring of force constant 180Nm−1. At the moment of release the ball has an additional downward speed of 3.0ms−1. The upper end of the spring is fixed to the ceiling and its lower end is directed downward. Neglect air resistance and the mass of the spring.
a. (i) Calculate the maximum compression produced in the spring during the subsequent motion of the ball.
b. (ii) Find the speed of the ball when the spring has returned to its natural (unstretched) length after the compression phase.