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??????

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....

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