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A particle is acted simultaneously by mu...

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

A

An ellipse

B

A parabola

C

A circle

D

A straight line

Text Solution

Verified by Experts

The correct Answer is:
C
Given, `x=acosomegat` . . . (i)
`y=a sin omegat` . . . (ii)
Squaring and adding eqs. (i) and (ii)
`x^(2)+y^(2)=a^(2)(cos^(2)omegat+sin^(2)omegat)=a^(2)`
`implies x^(2)+y^(2)=a^(2)" "[because cos^(2)omegat+sin^(2)omegat=1]`
This is the equation of a circle
Clearly, the locus is a circle of constant radius a.
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