2009: Problem 16

Topic: Oscillatory Motion
Concepts: CM frame, Effective spring constant, Mass-spring system

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Solution:

We go to the CM frame, where both masses oscillate about their midpoint. If we look at one of the masses (the other mass is the mirror reflection), it behaves as a mass-spring system with a half-spring. Since cutting a spring in half doubles the spring constant $k_e=2k$,

$$\omega=\sqrt{\frac{k_e}{m}}=\sqrt{\frac{2k}{m}}$$

so the answer is B.

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