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STD 11 - 13. oscillations — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 13. oscillations4 Marks
MCQ
A particle executes $S.H.M.$ and its position varies with time as $x=A$ sin $\omega t$. Its average speed during its motion from mean position to mid-point of mean and extreme position is
  • A
    zero
  • ✓
    $\frac{3 A \omega}{\pi}$
  • C
    $\frac{A \omega}{2 \pi}$
  • D
    $\frac{2 A \omega}{\pi}$
✓

Answer

Correct option: B.
$\frac{3 A \omega}{\pi}$
b
(b)

Phase at mean position $=0$

Phase at mid point

$\frac{A}{2}=A \sin \phi$

$\phi=\frac{\pi}{6}$

Time it takes to travel a phase difference of $\phi$

$t=\frac{2 \pi}{\omega} \times \frac{\phi}{2 \pi}$

or $t=\frac{\phi}{\omega}$

or $t=\frac{\pi}{6 \omega}$

Average speed $=\frac{\text { Total distance }}{\text { Time taken }}$

$=\frac{A / 2}{\pi / 6 \omega}$

$=\frac{3 A \omega}{\pi}$

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