Springs in Series Oscillation · CAP 2024 #9

Physics · mechanics

Problem

A mass hangs from the ceiling, held up by two springs in series. The upper spring has spring constant k1k_1, and the bottom spring has spring constant k2k_2. If the mass is displaced from equilibrium by a small amount xx, it has a maximum speed vv. If instead the mass is displaced by x/2x/2, what is the maximum speed? A. 14v\frac{1}{4}v B. 12v\frac{1}{2}v C. vv D. k1+k2k1k2v\frac{\sqrt{k_1+k_2}}{k_1k_2}v E. k1−k2k1k2v\frac{\sqrt{k_1-k_2}}{k_1k_2}v F. ∣k1−k2∣k1k2v\frac{|\sqrt{k_1-k_2}|}{k_1k_2}v

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