Angular frequency of a damped oscillator

In summary, angular frequency can be defined for a damped oscillator using the formula 2π/(2T), where T is the time between adjacent zero x-axis crossings. This definition is different from the usual definition for periodic motion, but it still has meaning for a given time period. This may seem illogical, but it is a valid way to define angular frequency for a damped oscillator.
  • #1
Tony Hau
101
30
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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  • #2
What seems illogical to you about that definition?
 

1. What is the definition of angular frequency for a damped oscillator?

The angular frequency of a damped oscillator is the rate at which the oscillations occur, measured in radians per second. It is denoted by the symbol ω (omega) and is equal to the square root of the spring constant divided by the mass of the oscillator.

2. How does the damping affect the angular frequency of a damped oscillator?

The damping in a damped oscillator reduces the amplitude of the oscillations over time, causing the angular frequency to decrease. This is because the damping force acts in the opposite direction of the motion, slowing down the oscillations.

3. What is the relationship between the angular frequency and the period of a damped oscillator?

The period of a damped oscillator is the time it takes for one complete oscillation. The angular frequency is inversely proportional to the period, meaning that as the angular frequency decreases, the period increases.

4. How does the initial amplitude affect the angular frequency of a damped oscillator?

The initial amplitude of a damped oscillator has no effect on the angular frequency. This is because the angular frequency is determined by the properties of the oscillator, such as the spring constant and mass, and not by the initial conditions.

5. Can the angular frequency of a damped oscillator be negative?

No, the angular frequency of a damped oscillator cannot be negative. It is always a positive value, representing the rate at which the oscillations occur. A negative angular frequency would result in an imaginary solution for the displacement of the oscillator, which is not physically possible.

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