A particle is placed at the lowest point of a smooth wire frame in the shape of a parabola, lying in the vertical $xy-$ plane having equation $x^2 = 5y$ $(x, y$ are in meter). After slight displacement, the particle is set free. Find angular frequency of oscillation.....$rad/s$ (in $rad/sec$ ) (take $g = 10\ m/s^2$ )
Diffcult
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$y=\frac{x^{2}}{5}$
$\frac{d y}{d x}=\frac{2 x}{5}$
$-m g \sin \theta=m \frac{d^{2} x}{d t^{2}}$
$\Rightarrow-g \frac{2 x}{5}=\frac{d^{2} x}{d t^{2}}$
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