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rogeralms
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Homework Statement
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?
Homework Equations
w^2 = k/m with w as the angular frequency
F= -kx = -(gradient) U
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.