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

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Correct option is C

Given, x=acos⁡ωt ……(i) y=asin⁡ωt ……..(ii)Squaring and adding Eqs. (i) and (ii),x2+y2=a2 cos2⁡ωt+sin2⁡ωt⇒ x2+y2=a2 ∵cos2⁡ωt+sin2⁡ωt=1This is the equation, of a circleClearly, the locus is a circle of constant radius a.

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A particle is acted simultaneously by mutually perpendicular simple harmonic motion.x=acos⁡ωt and y=asin⁡ωt. The trajectory of motion of the particle will be

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