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

Question

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

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Given, x $$=$$ a $$cos$$ ωt                                     …(i)            $$y=a$$ $$sin$$ ωt                                       …(ii)Squaring$$ and adding Eqs. $$(i) and (ii), we get           $$x2+y2=a2$$                      $$($$∵ $$cos2$$ωt $$+$$ $$sin2$$ ω$$t=1)This$$ is the equation of a circle.Clearly, the locus is a circle of constant radius a.

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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A particle is acted simultaneously by mutually perpendicular simple harmonic motion x = a cos ωt and y = a sin 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