Maximum extension?

Classical Mechanics Level pending

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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