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Potential Energy - Angular Frequency

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The potential energy of a one-dimensional mass m at a distance r from the origin is

U(r) = U_o(r/R + lambda^2(R/r)

for 0 < r < infinity, with U_o, R, and lambda all positive constants. Find the equilibrium position r_o. Let x be the distance from equilibrium and show that, for small x, the PE has the form U = const + 1/2(kx^2). What is the angular frequency of small oscillations?

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The potential energy of a one-dimensional mass m at a distance r from the origin is...

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