1. Tardigrade
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  3. Physics
  4. The potential energy of a particle of mass 1 kg in motion along the x -axis is given by: U=4(1- cos 2 x), where x is in metres. The period of small oscillation (in sec) is

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Q. The potential energy of a particle of mass $1 kg$ in motion along the $x$ -axis is given by: $U=4(1-\cos 2 x)$, where $x$ is in metres. The period of small oscillation (in sec) is

Oscillations

Solution:

$F=-\frac{d U}{d x}=-8 \sin 2 x$
For small oscillations,
$\sin 2 x=2 x$
i.e., $a=-16 x$
Since $a=-x$
the oscillations are SH in nature.
$T=2 \pi \sqrt{|\frac{x}{a}|} =2 \pi \sqrt{\frac{1}{16}}=\frac{\pi}{2} sec$