A particle of mass $5 × 10^{-5}\ kg$ is placed at lowest point of smooth parabola $x^2$ = $40y$ ($x$ and $y$ in $m$) (in $rad/s$). If it is displaced slightly such that it is constrained to move along parabola, angular frequency of oscillation will be approximately
Diffcult
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$\mathrm{F} =\mathrm{mg} \sin \theta $
$ \approx \mathrm{mg} \tan \theta $
$=\mathrm{mg} \frac{\mathrm{dy}}{\mathrm{dx}}=-\mathrm{mg} \times \frac{2 \mathrm{x}}{40} $
$\mathrm{a} =-\frac{\mathrm{x}}{2} \mathrm{m} $
$ \mathrm{a} =-\frac{-\mathrm{x}}{2} $
$ \omega =\frac{1}{\sqrt{2}} $
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