First slide

Simple hormonic motion

Question

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

Moderate

A

an ellipse
B

a parabola
C

a circle
D

a straight line

Solution

Given, $x = a \cos ωt$ …(i)
$y = a \sin ωt$ …(ii)
Squaring and adding Eqs. (i) and (ii), we get
$x^{2} + y^{2} = a^{2}$ $(∵ \cos^{2} ωt + \sin^{2} ωt = 1)$
This is the equation of a circle.
Clearly, the locus is a circle of constant radius a.

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