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  4. The equation of motion of a particle executing simple harmonic motion is a+16 π2 x=0 . In this equation, a is the linear acceleration in m s -2 of the particle at a displacement x in metre. The time period in simple harmonic motion is

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Q. The equation of motion of a particle executing simple harmonic motion is $a+16 \pi^{2} x=0 .$ In this equation, $a$ is the linear acceleration in $m \,s ^{-2}$ of the particle at a displacement $x$ in metre. The time period in simple harmonic motion is

Oscillations

Solution:

The given equation of $SHM$ is $a=-16 \pi^{2} x$
Standard equation of $SHM$ is $a=-\omega^{2} x$
Comparing two equations, we get $\omega=4 \pi$
$\therefore \,\,\,\,T=\frac{2 \pi}{\omega}=\frac{2 \pi}{4 \pi}=\frac{1}{2} s$