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 x2 = 5y(x, y are in meter and y axis is vertical). After slight displacement, the particle is set free. Find angular frequency of oscillation (in rad/sec) (take g = 10 m/s2)

Engineering

Physics

Simple Harmonic Motion

Question

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 x² = 5y(x, y are in meter and y axis is vertical). After slight displacement, the particle is set free. Find angular frequency of oscillation (in rad/sec) (take g = 10 m/s²)

6 rad/s

4 rad/s

2 rad/s

8 rad/s

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$ma = F = mgsinθ \approx mgtanθ = mg \frac{dy}{dx}$

$\frac{dy}{dx} = \frac{2 x}{5}$

$a = - g \times \frac{2 x}{5} = - 4 x$

ω = 2 rad/s

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