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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
The displacement of a particle is given at time $t$, by:$x=A \sin (-2 \omega t)+B \sin ^2 \omega t \quad$ Then,
  • ✓
    the motion of the particle is SHM with an amplitude of $\sqrt{A^2+\frac{B^2}{4}}$
  • B
    the motion of the particle is not SHM, but oscillatory with a time period of $T=\pi / \omega$
  • C
    the motion of the particle is oscillatory with a time period of $T=\pi / 2 \omega$
  • D
    the motion of the particle is a periodic.
✓

Answer

Correct option: A.
the motion of the particle is SHM with an amplitude of $\sqrt{A^2+\frac{B^2}{4}}$
a
(a)

The displacement of the particle is given by:

$x  =A \sin (-2 \omega t)+B \sin ^2 \omega t$

$=-A \sin 2 \omega t+\frac{B}{2}(1-\cos 2 \omega t)$

$=-\left(A \sin 2 \omega t+\frac{B}{2} \cos 2 \omega t\right)+\frac{B}{2}$

This motion represents SHM with an amplitude: $\sqrt{A^2+\frac{B^2}{4}}$, and mean position $\frac{B}{2}$

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