1. Tardigrade
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  3. Physics
  4. The potential energy of a particle of mass 2 kg in motion along the x-axis is given by U=2(1-c o s 2 x) J, where x is in meters. The period of small oscillations (in s ) is

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Q. The potential energy of a particle of mass $2\,kg$ in motion along the $x$-axis is given by $U=2(1-c o s$ $2 x) J$, where $x$ is in meters. The period of small oscillations (in $s$ ) is

Solution:

$U=2(1-\cos 2 x)$
$F=-\frac{d U}{d x}$
$F=-\frac{d}{d x}(2(1-\cos 2 x))$
$F=-4 \sin 2 x$
For small value of $x$
$\sin 2 x=2 x$
$F=-8 x ; a=-4 x$
$\omega=2$
$T=\frac{2 \pi}{\omega}$
$=\pi S$