Interesting Case Of Oscillations

Classical Mechanics Level 4

A block of mass \(m\) placed on a frictionless horizontal floor is connected to two identical springs each of force constant \(k\). The left end of the left spring is connected to a fixed support, and the right end of the right spring is free. Initially, the block is at rest, the springs are collinear and relaxed. If someone begins to pull the free end of the right spring with constant velocity \(u\) away from the wall, find much time \(t_u\) passes before the block acquires speed \(u\) for the first time, and what distance it moves in the time \(t_u\)?

Enter your answer as \(\dfrac {t_u}{d(t_u)} \).

Details and Assumptions

  • Take \(u = \SI{8}{\meter\per\second}\).

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