1. The problem statement, all variables and given/known data A mass moves along the x axis with potential energy U(x)= - U0 a^2 / (a^2 + x^2). What is the angular frequency assuming the oscillation is small enough to be harmonic? 2. Relevant equations w^2 = k/m with w as the angular frequency F= -kx = -(gradient) U 3. The attempt at a solution Since this is one-dimensional we take the derivative of U with respect to x. I get -(gradient) U = -2 U0 a^2 x / (a^2 + x^2)^2 Therefore k= 2 U0 a^2 / (a^2 + x^2)^2 The correct answer does not have an x term in it. w (omega) = k/m = (2 U0 / m a^2) ^ (1/2) Is there a binomial expansion that would essentially eliminate the x term in the denominator? Thanks for any help.