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Statement of a problem № 3115

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Consider a particle of mass m moving in one dimension under a force with the potential U (x ) = k(x^2-4xl ), where the constant k > 0. Show that the point x = 2l corresponds to a stable equilibrium position of the particle. Find the frequency of a small amplitude oscillation of the particle about the equilibrium position.

Solution:
Consider a particle of mass m moving in one dimension under a force with the pot

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