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JEE MAINS QUESTION........The function sin 2 (wt) represents????? a)a periodic but not shm with a period 2 pi/w b)a periodic,but not shm with a period pi/w c)a shm with a period 2pi/w d)a shm with a period pi/w ALSO, How to identify whether the particle is doing simple harmonic motion or periodic motion or both??????

JEE MAINS QUESTION........The function sin2(wt) represents?????
a)a periodic but not shm with a period 2 pi/w
b)a periodic,but not shm with a period pi/w
c)a shm with a period 2pi/w
d)a shm with a period pi/w                                                                                                                               ALSO,     How to identify whether the particle is doing  simple harmonic motion or periodic motion or both??????

Grade:11

2 Answers

Abhinab Nath
13 Points
4 years ago
Sin^2wt=1-cos2wt/2 ( since cos2α=1-2sin^2α so sin^2α=1-cos2α/2) =1/2-1/2cos 2wt So, it represents a periodic function with T=2π/2w =π/w but the function does not represents SHM.........the ans is (b) THANK YOU....
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

Sin^2wt=1-cos2wt/2
( since cos2α=1-2sin^2α so sin^2α=1-cos2α/2)
=1/2-1/2cos 2wt
So, it represents a periodic function with T= 2π/2w = π/w but the function does not represents SHM

Thanks and Regards

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