Consider the system described in Exercise 1. Suppose the parameter F is slowly varied from...

Consider the system described in Exercise 1. Suppose the parameter F is slowly varied from an initial value. What happens to the energy of the particle? The amplitude of oscillation? The period?

Exercise 1

A particle moves in periodic motion in one dimension under the influence of a potential V (x) = F |x|, where F is a constant. Using action-angle variables, find the period of the motion as a function of the particle’s energy.