Chapter 4.1, Problem 18P

Suppose that a mass $m$ slides without friction on a horizontal surface. The mass is attached to a spring with spring constant $k$, as shown in $\text{Figure}\text{4}\text{.1}\text{.10}$, and is also subject to viscous air resistance with coefficient $\gamma$ and an applied external force $F\left(t\right)$. Assuming that the force exerted on the mass by the spring obeys Hooke’s law, show that the displacement $x\left(t\right)$ of the mass from its equlibrium position satisfies Eq. $\left(18\right)$. How does the derivation of the equation of motion in this case differ from the derivation given in the text ?