Problem: A particle of mass m moves under the influence of a potential energy large{U(x) = frac{a}{x} + bx}, where a and b are positive constants and the particle is restricted to the region x > 0. Find a point of equilibrium for the particle and demonstrate that it is stable.

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A particle of mass m moves under the influence of a potential energy , where a and b are positive constants and the particle is restricted to the region x > 0. Find a point of equilibrium for the particle and demonstrate that it is stable.

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