Chapter 3, Problem 3.9P

A particle of mass m is at rest at the end of a spring (force constant = k) hanging from a fixed support. At t = 0, a constant downward force F is applied to the mass and acts for a time t₀. Show that, after the force is removed, the displacement of the mass from its equilibrium position (x = x₀, where x is down) is

$x-x_0\text{=}\frac{F}{k}[\cos {\omega }_0(t-t_0)-\cos {\omega }_{0}t]$

where ${\omega }_0^2\text{=}k\text{/}m\text{.}$