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Question

Two simple harmonic motions given by x=Asin(ωt+δ) and y=Asin(ωt+δ+π2) act on a particle simultaneously. Then the motion of particle will be:

A
circular anti-clockwise
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B
elliptical anti-clockwise
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C
elliptical clockwise
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D
circular clockwise
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Solution

The correct option is D circular clockwise
Given, x=Asin(ωt+δ) ...(i)
and y=Asin(ωt+δ+π2)
=Acos(ωt+δ) ...(ii)


Squaring and adding Eqs. (i) and (ii), we get
x2+y2=A2[sin2(ωt+δ)+cos2(ωt+δ)]
or x2+y2=A2
which is the equation of a circle.

Now, at (ωt+δ)=0,x=0,y=0
At (ωt+δ)=π2,x=A,y=0
At (ωt+δ)=π,x=0,y=A
At (ωt+δ)=3π2,x=A,y=0
At (ωt+δ)=2π,x=A,y=0
From the above data, we can see that the motion of the particle is a circle transversed in clockwise direction.
Hence, (d) is the correct answer.

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