question:-a particle of mass m is allowed to ocilate near the minimum of a vertical parabolic surface x^2=4ay,the angular frequency of smal ocilatons is given by:-

Dear Vishal,

Potential energy of the particle = mgy = mgx^2/(4a)As force = -dU/dxWe get force = -(mg/2a)*x = -kxgives k = mg/2aAngular frequency of oscillation omega = sqrt(k/m) = sqrt(g/2a)

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