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A particle is acted simultaneously by mu...

A particle is acted simultaneously by mutually perpendicular simple harmonic motions `x=acos 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
(c) Given , `x=a"cos"omegat" "…(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=1)`
`=a^(2)impliesx^(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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