The function  represents Option 1) a simple harmonic motion with a period  Option 2) a simple harmonic motion with a period  Option 3) a periodic, but not simple harmonic motion with a period Option 4) a periodic, but not simple harmonic motion with a period

$:\: y= \sin ^{2}\omega t= \frac{1-\cos 2\omega t}{2}= \frac{1}{2}-\frac{\cos 2\omega t}{2}$

It is a periodic motion but it is not  SHM

$\therefore \: Angular \: speed = 2\omega$

$\therefore \: period \: T= \frac{2\pi }{angular\: speed}= \frac{2\pi }{2\omega }= \frac{\pi }{\omega }$

Heance a periodic, but not simple harmonic motion with a period  is correct

$y=\sin ^{2}wt=\frac{1-\cos 2wt}{2}=\frac{1}{2}-\frac{\cos 2wt}{2}$

It is a periodic motion but it is not s.n

$\therefore$ Angular speed 2w

$\therefore$  period 2= $\frac{2\pi }{2w}$

$=\frac{\pi }{w}$

Option 1)

a simple harmonic motion with a period

Incorrect option

Option 2)

a simple harmonic motion with a period

Incorrect option

Option 3)

a periodic, but not simple harmonic motion with a period

Incorrect option

Option 4)

a periodic, but not simple harmonic motion with a period

Correct option

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