Chapter 4.10, Problem 8E

The response of an overdamped system to a constant force is governed by equation $\left(1\right)$ with $m=2$, $b=8$, $k=6$, $F_0=18$, and $\gamma =0$. If the system starts from rest $\left[y\left(0\right)=y^{\prime }\left(0\right)=0\right]$, compute and sketch the displacement $y\left(t\right)$. What is the limiting value of $y\left(t\right)$ as $t\to +\infty$? Interpret this physically.

$m\frac{d^{2}y}{d{t}^2}+b\frac{dy}{dt}+ky=F_0\cos \gamma t\mathrm{...}\left(1\right)$