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

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.