Question 140: Oscillations

Question

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

Accepted Answer

y =  sin
2
$\omega $t
= ${{1 - \cos 2\omega t} \over 2}$
$ = {1 \over 2} - {1 \over 2}\cos \,2\omega t$
$ 	herefore $ Angular speed = 2$\omega $
$ 	herefore $ Period (T) = ${{2\pi } \over {angular\,speed}}$ = ${{2\pi } \over {2\omega }}$ = ${\pi  \over \omega }$
So it is a periodic function.
As y =  sin
2
$\omega $t
${{dy} \over {dt}}$ = 2$\omega $sin$\omega $t cos$\omega $t = $\omega $ sin2$\omega $t
${{{d^2}y} \over {d{t^2}}}$ = $2{\omega ^2}$ cos2$\omega $t which is not proportional to -y.
Hence it is is not SHM.

Answer

a periodic, but not $SHM$ with a period ${\pi  \over \omega }$

Answer

a periodic, but not $SHM$ with a period ${{2\pi } \over \omega }$

Answer

a $SHM$ with a period ${\pi  \over \omega }$

Answer

a $SHM$ with a period ${{2\pi } \over \omega }$

Oscillations

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

Choose the correct answer: