Question

A mass m is in a potential energy profile U(x). Determine the equilibrium positions in the following situations, as well as the frequency of oscillations around stable equilibria:

1. U(x) = U0 (λx^(-12) – µx^(-6) ) (This simulates the interatomic potential energy in a solid, U0 in Joules, λ is in m12 and µ is in m6 )

2. U(x) = k.q.Q.x^(-1) + k.q.Q.(x-a)^(-1) (This would be the repulsive Coulomb potential of a charge q at position x, between two big charges Q located at positions x=0 and x=a)

3. U(x) = U0.(e^(-x/a) +λ.x/b) (U0 in Joules, a and b in meters, λ dimensionless)

Answer 1