An assembly of identical spring-mass systems | vedclass

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(C) If there were no collision,each spring-mass system would oscillate with a time period of $T_0 = 2 \pi \sqrt{\frac{m}{k}}$.Because of the elastic c

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$\pi \sqrt{\frac{m}{k}}$

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(C) If there were no collision,each spring-mass system would oscillate with a time period of $T_0 = 2 \pi \sqrt{\frac{m}{k}}$.Because of the elastic collision between the two masses,the masses are restricted from moving beyond their equilibrium positions towards each other. Each mass only performs half of its full oscillation cycle (the compression phase).Therefore,the time period of the oscillation of the system is half of the standard time period of a single spring-mass system.$T = \frac{T_0}{2} = \frac{1}{2} 	imes 2 \pi \sqrt{\frac{m}{k}} = \pi \sqrt{\frac{m}{k}}$.

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