The function  \sin ^{2}\left ( \omega t \right ) represents

  • Option 1)

    a simple harmonic motion with a period  \frac{2\pi }{\omega }

  • Option 2)

    a simple harmonic motion with a period  \frac{\pi }{\omega }

  • Option 3)

    a periodic, but not simple harmonic motion with a period \frac{2\pi }{\omega }

  • Option 4)

    a periodic, but not simple harmonic motion with a period \frac{\pi }{\omega }

 

Answers (1)

:\: 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  \frac{\pi }{\omega } 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  \frac{2\pi }{\omega }

Incorrect option

Option 2)

a simple harmonic motion with a period  \frac{\pi }{\omega }

Incorrect option

Option 3)

a periodic, but not simple harmonic motion with a period \frac{2\pi }{\omega }

Incorrect option

Option 4)

a periodic, but not simple harmonic motion with a period \frac{\pi }{\omega }

Correct option

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