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The displacement of a particle executing simple harmonic motion is given by y = A₀ + A sinωt + B cosωt. Then the amplitude of its oscillation is given by:

1. A₀ + √(A² + B²)
2. √(A² + B²)
3. √(A₀² + (A + B)²)
4. A + B

Correct answer: √(A² + B²)

Solution

In simple harmonic motion, the displacement is expressed as a combination of sine and cosine terms. The amplitude is given by the square root of the sum of the squares of the coefficients of the sine and cosine terms, which is √(A² + B²). The constant term A₀ does not affect the amplitude.

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