What is the underdamped frequency of an oscillation?

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A mass is attached to a spring in underdamped oscillation, the damped frequency is ω^2=( ω1 )^2 -(∂/2m)^2
where ω is the damped angular frequency
ω1 is the natural angular frequency
∂ frictional coefficient
m is the mass attached to the spring

is the damped angular frequency is constant throughout the oscillations ( I mean the angular oscillation is constant until the oscillation stop)
I think the oscillation should not oscillate with constant angular damped frequency. but the formula of damped oscillation is not varies with time so is that constant??

thank you.
 
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