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13. oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics13. oscillations1 Mark
MCQ
A body oscillates with a simple harmonic motion having amplitude $0.05\, m .$ At a certain instant, its displacement is $0.01\, m$ and acceleration is $1.0 \,m / s ^{2} .$ The period of oscillation is
  • A
    $0.1 \,s$
  • B
    $0.2 \,s$
  • C
    $\frac{\pi}{10}\, s$
  • ✓
    $\frac{\pi}{5}\, s$
✓

Answer

Correct option: D.
$\frac{\pi}{5}\, s$
d
The angular frequency is given as,

$| a |=\omega^{2} y$

$1=\omega^{2} \times 0.01$

$\omega^{2}=\frac{1}{0.01}=100$

$\omega=10 rad / s$

The time period comes out to be,

$T =\frac{2 \pi}{\omega}$

$T =\frac{2 \pi}{10 rad / s }=\frac{\pi}{5} sec$

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