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  4. A particle of mass 4 kg moves simple harmonically such that its PE ( U ) varies with position x, as shown. The period of oscillations is:-

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Q. A particle of mass $4\, kg$ moves simple harmonically such that its $PE ( U )$ varies with position $x$, as shown. The period of oscillations is:-Physics Question Image

Oscillations

Solution:

$U_{\max }=\frac{1}{2} kx ^{2}$
$1=\frac{1}{2} k (0.2)^{2}$
$ \Rightarrow k =50$
and $T =2 \pi \sqrt{\frac{ m }{ k }} $
$\Rightarrow T =2 \pi \sqrt{\frac{4}{50}}=\frac{2 \pi \sqrt{2}}{5} \sec$