Question

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

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

Answer 1

The correct option is D a circle

Formula used: ${\cos }^2\omega t+{\sin }^2\omega t=1$

Given: $x=a\cos \omega t$ and $y=a\sin \omega t$

Given relation are of $x$ and $y$ with time $t$

Squaring and adding Equations $\left(i\right)$ and $\left(ii\right)$,

$x^2+y^2=a^2({\cos }^2\omega t+{\sin }^2\omega t$

$x^2+y^2=a$

This is the equation, of a circle Clearly, the locus is a circle of constant radius $a$.