Answer
Since the value of $k$ is proportional to $m$, the angular frequency of a pendulum is independent of the mass.
$\omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{m~g}{L~m}} = \sqrt{\frac{g}{L}}$
Work Step by Step
For a simple pendulum, $\omega = \sqrt{\frac{g}{L}}$
Suppose that $\omega$ has the form $\sqrt{\frac{k}{m}}$. We can find an expression for $k$:
$\frac{k}{m} = \frac{g}{L}$
$k = \frac{mg}{L}$
Since the value of $k$ is proportional to $m$, the angular frequency of a pendulum is independent of the mass.
Note that $\omega = \sqrt{\frac{k}{m}} = \sqrt{\frac{m~g}{L~m}} = \sqrt{\frac{g}{L}}$
