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

Moderate

A

an ellipse
B

a parabola
C

a circle
D

a straight line

Solution

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

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