A 2.00-kg bucket containing 10.0 kg of water is hanging from a vertical ideal spring of force constant 125 N/m and oscillating up and down with an amplitude of 3.00 cm. Suddenly the bucket springs a leak in the bottom such that water drops out at a steady rate of 2.00 g/s. When the bucket is half full, find
(a) The period of oscillation and
(b) The rate at which the period is changing with respect to time. Is the period getting longer or shorter?
(c) What is the shortest period this system can have?