An assembly of identical spring-mass systems | vedclass

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(C) Each mass is attached to a spring of constant $k$ and has mass $M$. When displaced and released,each mass performs simple harmonic motion $(SHM)$

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$2\pi \sqrt {\frac{M}{k}} $

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(C) Each mass is attached to a spring of constant $k$ and has mass $M$. When displaced and released,each mass performs simple harmonic motion $(SHM)$ independently until they collide.The time period for a single spring-mass system is $T = 2\pi \sqrt{\frac{M}{k}}$.Since the collision is elastic and the masses are identical,they exchange velocities upon collision. Effectively,each mass completes half of its oscillation cycle before colliding with the other,and then reverses its motion.The total time period of the system's oscillation is the sum of the time taken for half an oscillation of the left mass and half an oscillation of the right mass.$T_{total} = \frac{T}{2} + \frac{T}{2} = T = 2\pi \sqrt{\frac{M}{k}}$.

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