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Statement of a problem № 3393

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A particle of mass m is located in a one-dimensional potential field U(x) = a/x^2 - b/x x where a and b are positive constants. Show that the period of small oscillations that the particle performs about the equilibrium position will be T = 4pi·sqrt(2a^3m/b^4)

Solution:
A particle of mass m is located in a one-dimensional potential field U(x) = a/x^

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