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

a) an ellipse

b) a parabola

c) a circle

d) a straight line

Answer:

The correct option is c) a circle

Given

x=acosωt                                         (i) 

y=asinωt                                          (ii)

Squaring and adding above two equations, we get:

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

{{x}^{2}}+{{y}^{2}}={{a}^{2}}

It is a circle equation. As a result, the motion will follow a circular path.