I don\'t understand how to calculate maximum elongation of a spring. For example

Question

I don't understand how to calculate maximum elongation of a spring. For example, let's say there was a box attached to an end of a horizontal spring and we need to find the maximum elongation of the spring if at its equilibrium length the box is given a speed of 10 m/s. Mass of the box is 1 kg and spring constant 100 N/m.

I don't understand how to even set this problem up. What does it mean that the box is given a speed when the spring is at equilibrium length?

Explanation / Answer

This is an energy conservation problem let the spring is stretched by max length x Potential energy stored in the spring = .5kx^2 Now when the spring is stretched maximum the kinetic energy is zero so by energy conservation Initial kinetic energy = max stretch potential energy .5mv^2 = .5kx^2 1*10^2 = 100x^2 => x = 1m The statement that the box is given a speed when the spring is at equilibrium length means that spring is in a relaxed state at that instant and no potential energy is stored in it so that we can apply the energy conservation law without worrying about the initial potential energy

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