Why is the damping force larger than the restoring force in this model? I'm reading the book "Differential equations with boundary-value problems" by D.Zill and I cannot understand the following:

In the Free Damped Motion Model,



we have a flexible spring suspended vertically from a rigid support.  We attach an object of certain mass $m$  to the spring so this is stretched $s$ units (in this situation, the object will be in an equilibrium position).   Assume that there is a resisting force due to the surrounding medium (as  a viscous medium, for example).  If $x(t)$ is the position of the object after $t$ time units, we have the ODE $$mx''=mg-\underset{Hooke\; Law}{\underbrace{k(x+s)}}-\underset{damping\; force}{\underbrace{\beta x'}},$$ where $g$ is the gravity acceleration , $k$ is the constant given by the Hooke Law (restoring force) and $\beta&gt;0$ is the damping -constant given by the damping force.

The ODE has as solutions for its auxiliary equation:  $-\lambda\pm \sqrt{\lambda^2-\omega^2}$, where $\lambda=\beta/(2m), \omega^2=k/m$.  

We have three cases to analyze, but it is one that I cannot get: 

If $\lambda^2-\omega^2&gt;0$, then * the system is said to be overdamped
because the damping coefficient b is large when compared to the spring constant k.*

Why does the author state that $b$ is large when compared to $k$?  I cannot get why he affirms this (which I guess he does in order to conclude that the damping force is large compared to the restoring force).  I know that the graph of the solutions helps to visualize the model but I want to understand this model just by looking at the equation and its variable involved (basically, a qualitative analysis of the problem).
Starting with the inequality $\lambda^2-\omega^2&gt;0$, plug in the definitions of $\lambda$ and $\omega$ in terms of $\beta$, $k$, and $m$.  Then simplify the resulting inequality to get all the $\beta$'s on one side and all the $k$'s on the other.
Starting with the inequality $\lambda^2-\omega^2&gt;0$, plug in the definitions of $\lambda$ and $\omega$ in terms of $\beta$, $k$, and $m$.  Then simplify the resulting inequality to get all the $\beta$'s on one side and all the $k$'s on the other.