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