The function ^2 ( t) represents - Vidyadip

MCQ

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

A
A simple harmonic motion with a period $2\pi /\omega $
B
A simple harmonic motion with a period $\pi /\omega $
C
A periodic but not simple harmonic motion with a period $2\pi /\omega $
✓
A periodic but not simple harmonic, motion with a period $\pi /\omega $

✓

Answer

Correct option: D.

A periodic but not simple harmonic, motion with a period $\pi /\omega $

d
(d) $y = {\sin ^2}\omega \,t$$ = \frac{{1 - \cos 2\omega t}}{2}$

==> Period,$T = \frac{{2\pi }}{{2\omega }} = \frac{\pi }{\omega }$

The given function is not satisfying the standard differential equation of $S.H.M.$

$\frac{{{d^2}y}}{{d{x^2}}} = - \,{\omega ^2}y$. Hence it represents periodic motion but not $S.H.M.$

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