Estimating a Central Potential as a Spring Potential

Question

The potential energy of a one-dimensional mass m at a distance r from the origin is U(r) = U0 (r/R + C2R/r) for 0 < r < ∞, with R, C and U0 all positive constants.

a) Find the equilibrium position r0.

b) Let x be the distance from equilibrium and show that, for small x (x << 1), the potential energy can be expressed as U = constant + ½kx2 .

c) What is the angular frequency of a small oscillation? Your answer should be in terms of m, R, C and U0 and may be some fundamental constants.

Answer 1