A mass point m hangs at one end of a vertically hung Hooke’slaw spring of force constant k. The other end of the spring is oscillates up and down according to z1 = a cos ω1t. By treating a as a small quantity, obtain a first order solution to the motion of m in time, using time dependent perturbation theory. What happens as ω1 approaches the unperturbed frequency ω0?

This is question 12.2 from the book "Classical Mechanics", from Herbert Goldstein

The answer is on Chegg (http://www.chegg.com/homework-help/mass-point-m-hangs-one-end-vertically-hung-hooke-s-law-sprin-chapter-12-problem-2e-so...) . Can anybody help me? Thanks!

(won't mind if you charge a little bit more for the answer)