The potential energy of a one-dimensional mass m at a distance r from the origin is
U(r)=U r +λ2R oRr
for 0 < r < ∞, with Uo, R, and λ all positive constants. Find the equilibrium position ro. Let x be the
distance from equilibrium and show that, for small x, the PE has the form U = const + 1 kx2. What is 2
the angular frequency of small oscillations?