A block of mass M is tied to a spring of force constant K and the system is suspended vertically. Consider three situations shown in fig. (a), (b) and (c).
(a) In fig. (a), an insect of mass M is clinging to the block and the system is in equilibrium. The insect leaves the block and falls. Find the amplitude of resulting oscillations.
(b) In fig. (b), an insect of mass M is resting on the top of the block and the system is in equilibrium. The insect suddenly jumps up with a speed `u=gsqrt((M)/(K))` and the block starts oscillating. Find amplitude of oscillation assuming that the insect never falls back on the block
(c) In fig. (c), an insect of mass M falls on the block this in equilibrium. The insect hits the block with velocity `u=gsqrt((M)/(K))` while moving downwards sticks to the block. Find the amplitude of oscillation.

Answer

(a) `(Mg)/(K)`
(b) `sqrt(2) (Mg)/(K)`
(c) `(sqrt(6))/(2)(Mg)/(K)`