Two simple harmonic motions act on a particle. These harmonic

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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 , the resulting motion is
2

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

Correct Option: D

x = A cos (ωt + δ)
y = A cos (ωt + α) .........(1)
Squaring (1) and (2) and then adding
x² + y² = A² [cos² (ωt + α) + sin² (ωt + α)]
or x² + y² = A² , which is the equation of a circle. The present motion is anticlockwise.

, y = A cos (ωt + α) when δ = α +	π	, the resulting motion is
	2