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 $x =a \,cos \omega t \quad ...(i)$ $y=a\, sin \omega t \quad ...(ii)$ Squaring and adding $(i)$ and $(ii)$, we get $x^2 + y^2 = a^2cos^2\omega t + a^2sin^2\omega t = a^2$ It is an equation of circle. Thus, trajectory of motion will be circle.