Question

A 2.0 kg bucket is attached to a horizontal ideal spring and rests on frictionless ice. You have a 1.0 kg mass that you must drop into the bucket. Where should the bucket be when you drop the mass (so it is moving purely vertically when it lands in the bucket) if your goal is to: (a) Maximize the amplitude of the oscillation of the resulting 3.0 kg mass and spring system. (b) Minimize the amplitude of the oscillation of the resulting 3.0 kg mass and spring system.

Answer 1

(a) The total mass acting on the spring is, M = 2 kg+1 kg = 3 kg The force on the spring is equal to the weight on the spring. ma = mg a= 8 The relation between acceleration and spring is, a=wA g=m*A ME = 1 A = Mg _(3 kg)(9.8 m/s2)

(a) The maximize amplitude is, 29.4N 29.4N (2 kg) (9.8 m/s) = 1.5x (b) The maximize amplitude is, A = 29,4 N 29.4 N * (3kg)(9.8m/s?)