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When two displacements represented by y₁ = a sin(ωt) and y₂ = b cos(ωt) are superimposed the motion is:

1. simple harmonic with amplitude a/b
2. simple harmonic with amplitude √(a² + b²)
3. simple harmonic with amplitude (a + b)/2
4. not a simple harmonic

Correct answer: simple harmonic with amplitude √(a² + b²)

Solution

The superposition of y₁ = a sin(ωt) and y₂ = b cos(ωt) results in a single simple harmonic motion with amplitude √(a² + b²), as these are orthogonal components of the same frequency.

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