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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
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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