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A particle undergoing SHM has an amplitude of 3 cm. When the particle is at x = 2 cm, find the magnitude of its velocity.

1. √5 cm/s
2. 4π/√5 cm/s
3. 2π/√5 cm/s
4. π/√5 cm/s

Correct answer: 2π/√5 cm/s

Solution

In SHM, the velocity at a displacement x is given by v = ω√(A² - x²), where A is the amplitude and ω is the angular frequency. Substituting A = 3 cm and x = 2 cm, the velocity simplifies to v = ω√(9 - 4) = ω√5. Since ω is not provided, the answer must be expressed in terms of ω. Option C matches this form.

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