The equation of $SHM$ of a particle is given as
$2\,\frac{{{d^2}x}}{{d{t^2}}} + 32x = 0$
where $x$ is the displacement from the mean position of rest. The period of its oscillation (in seconds) is
Diffcult
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The given equation of $SHM$ is,
$2 \frac{\mathrm{d}^{2} \mathrm{x}}{\mathrm{dt}^{2}}+32 \mathrm{x}=0 \quad \mathrm{OR}$
$\frac{d^{2} x}{d t^{2}}+\frac{32}{2} x=0$
$\frac{d^{2} x}{d t^{2}}=-16 x$ $...(i)$
The standard equation of $SHM$ is,
$\frac{d^{2} x}{d t^{2}}=-\omega^{2} x$ $...(ii)$
Comparing equation, $(i)$ and $(ii),$ we get
$\omega^{2}=16 \quad \mathrm{OR}$ $\omega=4$
The period, $T=\frac{2 \pi}{\omega}=\frac{2 \pi}{4}=\frac{\pi}{2} \mathrm{s}$
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