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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
6 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
3 years 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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