A particle of mass 5 × 1 0 − 5 kg is placed at the lowest point of a smooth parabola having the equation 20 x 2 = y (x, y in m). Here y is the vertical height. If it is displaced slightly and it moves

Question

A particle of mass 5 × 1 0 − 5 kg is placed at the lowest point of a smooth parabola having the equation 20 x 2 = y (x, y in m). Here y is the vertical height. If it is displaced slightly and it moves such that it is constrained to move along the parabola, the angular frequency of oscillation will be, (in rad/s).

TestHub · Accepted Answer

Near the bottom the parabola y = 20 x 2 has radius of curvature ρ = 2 × 20 1 ​ = 40 1 ​ m. Small oscillations along the surface behave like a pendulum of length ρ : ω = ρ g ​ ​ = 9.8 × 40 ​ = 392 ​ ≈ 19.8 rad/s. To two significant figures, ω = 20 rad/s.

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