A body is attached to the lower end of a vertical spiral spring and it is gradually lowered to its equilibrium position. This stretches the spring by a length x. If the same body attached to the same spring is allowed to fall suddenly, what would be the maximum stretching in this case
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When spring is gradually lowered to it's equilibrium position
kx = mg ∴ ∴ 
.
When spring is allowed to fall suddenly it oscillates about it's mean position
Let y is the amplitude of vibration then at lower extreme, by the conservation of energy
⇒ ⇒ 
⇒ ⇒ 
= 2x.
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