First slide

Simple hormonic motion

Question

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:

Easy

A

a circle
B

a straight line
C

an ellipse
D

a parabola

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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