A1.50 kg bucket containing 12.0 kg of water is hanging from a vertical ideal spring of force constant 450 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.
(d) is the period getting longer or shorter?
(c) what is the shortest period this system can have?

The great sandini is a 60.0-kg circus performer who is shot from a cannon (actually a spring gun). you don’t find many men of his caliber, so you him design a new gun. this new gun has a very large spring with a very small mass and a force constant of 1100 n/m that he will compress with a force of 4400 n. the inside of the gun barrel is coated with teflon, so the average friction force will be only 40.0 n during the 4.00 m he moves in the barrel. at what speed will he emerge from the end of the barrel, 2.50 m above his initial rest position?