Question

A particle is acted simultaneously by mutually perpendicular simple harmonic motions x = a cos $\omega$t and y = a sin $\omega$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

Answer: (C)

A circle

Answer 2

Given

$x = a\cos\omega t$ …… (i)

$y = a\sin\omega t$ ……. (ii)

Squaring and adding (i) and (ii) we get

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

It is equation of circle thus trajectory of motion will be circle