Question

A particle is acted simultaneously by mutually perpendicular simple harmonic motions $x=acos\omega t$ and $y=asin\omega t$. The trajectory of motion of the particle will be

• A. an ellipse
• B. a parabola
• C. a circle
• D. a straight line

Answer 1

The correct option is C a circle

Given
$x=acos\omega t$ ......(i)
$y=asin\omega t$ ......(ii)
Squaring and adding (i) and (ii), we get
$x^2+y^2=a^{2}co{s}^2\omega t+a^{2}si{n}^2\omega t=a^2$
It is an equation of circle. Thus, trajectory of motion will be circle.