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Two mutually perpendicular linear simple harmonic motions of equal amplitude and frequency are imposed on a particle along x and y axis respectively. The initial phase difference between them is π/2. The resultant path followed by the particle is:

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a circle

a straight line

an ellipse

a parabola

answer is A.

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Detailed Solution

Let the component SHM's be x = A cos ωt and y = A cos(ωt - π/2)

$\therefore y = A\sin \omega t{\left( {\frac{x}{A}} \right)^2} + {\left( {\frac{y}{A}} \right)^2} = {\cos ^2}\omega t + {\sin ^2}\omega t$

$\Rightarrow {x^2} + {y^2} = {A^2}$

The equation represents a circle of radius A with its centre at the origin.

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