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 clockwiseGiven, 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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