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Two simple harmonic motions act on a particle. These harmonic motions are x = A cos (ωt + δ), y = A cos (ωt + α) when δ = α ± π/2, the resulting motion is

1. a circle and the actual motion is clockwise
2. an ellipse and the actual motion is counterclockwise
3. an ellipse and the actual motion is clockwise
4. a circle and the actual motion is counterclockwise

Correct answer: a circle and the actual motion is counterclockwise

Solution

When the phase difference between two SHMs is ±π/2 and their amplitudes are equal, the resultant motion is a circle. The direction of motion depends on the sign of the phase difference. For δ = α + π/2, the motion is counterclockwise.

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