# Simple harmonic motion + rate of changes

Carnauba
A bucket of mass 2.0 kg containing 10 kg of water is hanged on a vertical ideal spring with constant 125 N/m, oscillating up and down with an amplitude equal to 3.0 cm.
Suddenly arises a leaky in the bottom of the bucket so that the water flows at constant rate of 2.0 grams/s. When the bucket is half full:

a) determine the period of oscillation and the rate at which the period varies with time.
b) What is the shortest period that this system can have?