# Angular frequency of a damped oscillator

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## Main Question or Discussion Point

So in my textbook on oscillations, it says that angular frequency can be defined for a damped oscillator. The formula is given by:
Angular Frequency = 2π/(2T), where T is the time between adjacent zero x-axis crossings.
In this case, the angular frequency has meaning for a given time period.

Okay, what I do not understand is that normally, angular frequency is something defined for periodic motion, in which the oscillator passes twice through a given point with the same velocity and completes a whole cycle. Why is it also feasible to define a period for damped oscillator as it will never passes through a given point obviously. Secondly, what does the sentence 'has meaning for a given time period' exactly mean?

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PeroK
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What seems illogical to you about that definition?