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An assembly of identical spring-mass systems is placed on a smooth horizontal surface as shown. At this instant, the springs are relaxed. The left mass is displaced to the/left and theiright mass is displaced to the right by same distance and released. The resulting collision is elastic. The time period of the oscillations of system is
$2 \pi \sqrt{\frac{2 m}{k}}$
$2 \pi \sqrt{\frac{m}{2 k}}$
$\pi \sqrt{\frac{m}{k}}$
$2 \pi \sqrt{\frac{m}{k}}$
Solution
(c)
If there was no collision each spring will oscillate with period
$T=2 \pi \sqrt{\frac{m}{k}}$
Because of collisions the springs are only compressed but cannot extend beyond their natural length. Hence the perform only half oscillation.
Hence $\quad T=2 \pi \sqrt{\frac{m}{k}} \div 2$
or $T=\pi \sqrt{\frac{m}{k}}$
