First slide

Simple hormonic motion

Question

A particle is acted simultaneously by mutually perpendicular simple harmonic motion x = a cos ωt and y = a sin ωt. The trajectory of motion of the particle will be

Easy

A

an ellipse
B

a parabola
C

a circle
D

a straight line

Solution

$x = a\cos \omega t$
$y = a\sin \omega t$
$\therefore {x^2} + {y^2} = {a^2}\left( {{{\cos }^2}\omega t + {{\sin }^2}\omega t} \right)$
$\Rightarrow {x^2} + {y^2} = {a^2}$
The above equation represents a circle of radius 'a' with its centre at the origin.

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