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
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
elliptical anti-clockwise
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
elliptical clockwise
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
circular clockwise
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
Open in App
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.