A particle of mass m is allowed to oscillate near the point of minima of a vertical parabolic path having the equation x 2 = 4 a y , where x - a x i s is along the horizontal direction and y - a x i s

Question

A particle of mass m is allowed to oscillate near the point of minima of a vertical parabolic path having the equation x 2 = 4 a y , where x - a x i s is along the horizontal direction and y - a x i s is along the vertical direction. The angular frequency of small oscillations of the particle is

TestHub · Accepted Answer

ma = - mg sin θ a = - g sin θ or a = - g tan θ ...(i) (as θ is small) Now, x 2 = 4 ay ∴ dy dx = x 2 a ∴ a = - g x 2 a - ω 2 x = - gx 2 a ω = g 2 a

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