A pendulum is hung from the roof of a sufficiently high building and is moving freely to and fro like a simple harmonic oscillator. The acceleration of the bob of the pendulum is $20\; m/s^2$ at a distance of $5\; m$ from the mean position. The time period of oscillation is
NEET 2018, Medium
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Magnitude of acceleration of a particle moving in a $SHM$ is, $|a|=\omega^{2} y ;$ where $y$ is amplitude.
$\Rightarrow \quad 20=\omega^{2}(5) \Rightarrow \omega=2 \mathrm{rad} \mathrm{s}^{-1}$
$\therefore \quad$ Time period of oscillation, $T=\frac{2 \pi}{\omega}=\frac{2 \pi}{2}=\pi \mathrm{s}$
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