A ball of mass m falls freely from the ground at height h and touches a spring of height h0. The coefficient of the spring is k. Find the length of the ball compressed and how long it takes for the ball's speed to become zero and how long it takes for the ball to return to height h0

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Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be created or destroyed — only transformed.