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Oscillations

Question

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A particle executing simple harmonic motion of amplitude 5 cm has maximum speed of 31.4 cm/s. The frequency of its oscillation is

3 Hz

2 Hz

4 Hz

1 Hz

Solution

D.

1 Hz

The maximum speed of a particle executing SHM is

$u_{\max} = aω = a (2 πn) n = \frac{u_{\max}}{2 πa} Here, u_{\max} = 31.4 cm / s, a = 5 cm$

substituting the given values, we have

$n = \frac{3.14}{2 \times 3.14 \times 5} n = 1 Hz$

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