A mass m suspended from a vertical spring oscillates with frequency f. If the spring is cut in half and the same mass m is suspended from one of the halves, what is the new oscillation frequency f'?
Answer and explanation
Correct answer: A. sqrt(2) * f
- Step 1: When a spring is cut in half, each half has twice the original spring constant: k' = 2*k.
- Step 2: The frequency of a mass-spring system is f = (1 / (2pi)) sqrt(k / m).
- Step 3: The new frequency is f' = (1 / (2pi)) sqrt(k' / m) = (1 / (2pi)) sqrt(2k / m) = sqrt(2) f.
Answer
sqrt(2) * f.
Why not the others: 2 * f neglects the square root dependence on spring constant; f / sqrt(2) assumes the spring constant halved; f / 2 assumes the spring constant quartered.
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