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Question

A particle undergoes mutually perpendicular simple harmonic motions given by x=acosωt and y=asinωt. The trajectory of motion of the particle will be

A
an ellipse
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B
a parabola
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C
a circle
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D
a straight line
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Solution

The correct option is C a circle
Given the SHM equations in x and y directions are
x=acosωt ........(i)
y=asinωt ........(ii)
Squaring and adding equations (i) and (ii), we get
x2+y2=a2(cos2ωt+sin2ωt)
x2+y2=a2
[cos2ωt+sin2ωt=1]
This is the equation of a circle of radius a with centre at the origin.
Hence, the trajectory of motion of the particle will be a circle.

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