# Maximum extension?

Two small spheres of mass $$1\text{ kg}$$ each are connected to each other by means of an unstretched spring of force constant $$k=100\text{ N/m}$$ and natural length $$2.4\text{ m}$$.

The system is placed on a smooth horizontal surface and the two spheres are given velocity $$v$$ as shown in the figure below. The maximum elongation in spring is found to be $$0.4\text{ m}$$ during subsequent motion.

Calculate $$v$$ in $$\text{m/s}$$. Take $$\sqrt{31} = 5.6$$.

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