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PART - 2 CH - 13 Oscillations — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysicsPART - 2 CH - 13 Oscillations2 Marks
Question
The time period of a simple harmonic oscillator is 6 seconds. How much time will it take for the oscillator to start moving from the equilibrium position? After that its displacement will be half of its amplitude?
✓

Answer

$x=A \sin \frac{2 \pi}{T} t$
Here is $T=6$ second and
$x=\frac{1}{2} A$
Then $\quad \frac{A}{2}=A \sin \frac{2 \pi}{6} t$
$\frac{1}{2}=\sin \frac{2 \pi t}{6}=\sin \frac{\pi t}{3}$
$\sin \frac{\pi}{6}=\sin \frac{\pi t}{3}$
$\frac{\pi}{6}=\frac{\pi t}{3}$
$T=\frac{3 \pi}{6 \pi}=\frac{1}{2}$ second

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