What is the underdamped frequency of an oscillation?

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In underdamped oscillation, the damped frequency is defined by the equation ω^2=(ω1)^2-(∂/2m)^2, where ω is the damped angular frequency, ω1 is the natural angular frequency, ∂ is the frictional coefficient, and m is the mass. The damped angular frequency remains constant throughout the oscillations until they cease, confirming that it does not vary with time. This characteristic distinguishes underdamped oscillation from other types, where oscillations do not occur. The discussion clarifies that while the oscillation persists, the damped frequency itself remains stable. Understanding these principles is essential for analyzing harmonic oscillators in physics.
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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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