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Is it possible to solve spring questions with Calculus?

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I found this on a previous thread and someone mentions that you can use calculus to solve it. I already solved it using the law of conservation and got .027816 m or 2.7 cm, but it's driving me nuts figuring out how to use calculus to solve.

How do I go about integrating acceleration since it's dependent on distance? Please give any insight.

1. A block of mass 0.3 kg and spring constant 24 N/m is on a frictionless surface. If the block is set into motion when compressed 3.5 cm, what is the maximum velocity of the block? How much is the spring compressed when the block has a velocity of 0.19 m/s?

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