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Masses Mₐ and Mₐ hanging from the ends of strings of lengths Lₐ and Lₐ are executing simple harmonic motions. If their frequencies are fₐ = 2fₐ, then:

1. Lₐ = 2Lₐ and Mₐ = Mₐ/2
2. Lₐ = 4Lₐ regardless of masses
3. Lₐ = 2Lₐ and Mₐ = 2Mₐ
4. Lₐ = 4Lₐ regardless of masses

Correct answer: Lₐ = 4Lₐ regardless of masses

Solution

The frequency of a simple pendulum is inversely proportional to the square root of its length, and it is independent of the mass. Since fₐ = 2fₐ, the length Lₐ must be four times Lₐ to satisfy the relationship f ∝ 1/√L.

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