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The frequency of vibration f of a mass m suspended from a spring of spring constant k is given by a relation of the type \( f = c m^x k^y \), where c is a dimensionless constant. The values of x and y are

1. x = 1/2, y = -1/2
2. x = -1/2, y = 1/2
3. x = 1/2, y = 1/2
4. x = -1/2, y = -1/2

Correct answer: x = -1/2, y = 1/2

Solution

Using dimensional analysis, the frequency f has dimensions [T⁻¹]. For f = c m^x k^y, the dimensions of m are [M], and the dimensions of k are [M T⁻²]. Equating dimensions, we find x = -1/2 and y = 1/2.

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