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start new year with a tough problem

In a box there is a weight fixed to a spring. Both the box and the weight have equal mass M. The mass of the spring is negligible and its constant is k. The box is dropped down freely from a height h so that during the falling the weight is in equilibrium. Colliding with a soft surface the box stays still for a moment. The box is high enough for the weight not to collide against the box. Not for one moment is the spring completely pressed together. — a) What is the smallest dropping height hm for the box to jump back up again? — b) The box was dropped from a height H ≈ H m found in the last part. For what time T will the box be on the ground before starting to rise up?

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