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: