Singular behavior of the density state called a van Hove singularity

[JordanGo]

Homework Statement

I was doing a condensed matter problem (3rd year) of a phonon dispersion relation for a monatomic linear chain. It asked told me to derive an expression for the density state per unit length and I obtained the following:
$g(\omega) = \frac{L}{a\p} \frac{1}{4C/M - \omega^{2}}$

Homework Equations

The singularity occurs at
$\omega = 2(\frac{C}{M})^{1/2}$

The Attempt at a Solution

Can someone explain the origin of this singularity?

 

[Nate810]

I understand that a singularity occurs when the denominator becomes zero and hence you get an infinite value for the corresponding function. But how does this relate to the problem?