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 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 ?
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