What is the Unit of ω=sqrt(g/x0) and How is it Converted to Radians?

[Barrowlands]

So, I'm trying to brush up on my undergrad physics, and I'm sure this is a bone-headed question, so please bear with me.

Homework Statement

A heavy object, when placed on a rubber pad that is to be used as a shock absorber, compresses the pad by 1cm. If the object is given a vertical tap, it will oscillate. Ignoring the damping, estimate the oscillation frequency. [The book I'm using actually gives the solution]

Homework Equations

x(t)=A*sin(sqrt(k/m)t+$\phi$)
ω=sqrt(k/m)
F=k|l-l0|

The Attempt at a Solution

We'll call x0 the equilibrium displacement, x0=1cm
k=spring constant of rubber
so
k(l-l0)=k*x0=mg (equilibrium)
gives us
k=(mg)/(x0)
then
ω=sqrt(k/m)
which eventually solves to
ω=sqrt(g/x0)

The book gives an answer of sqrt(980) rad/s. My question is given the units from ω=sqrt(g/x0) (meters, seconds, centimeters), how do they arrive at radians?

Edit: I just realized I put this in the wrong sub-forum, my apologies.

 

[voko]

The unit of sqrt (g/x0) is s^-1. A "radian" is not really a unit, it is merely an indication that the corresponding dimensionless value is used as an angular measure.