A mass point m hangs at one end of a vertically hung Hooke's-law spring of force constant k. The other end of the spring is oscillated up and down according to z ₁ = acosω ₁ t. 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 ω ₁ approaches the unperturbed frequency ω ₀ ?