Finding angular frequency of damped oscillation

In summary, the conversation discusses finding the angular frequency of a spring-mass system given the damping constant, mass of the object at the end of the spring, mass of the spring, and spring constant. The formula for angular frequency is the square root of the spring constant over the mass at the end of the spring, but there is confusion about how to factor in the mass of the spring. The provided link discusses the concept of effective mass in a spring-mass system.
  • #1
striker300
8
0
My question is that I am asked to find the angular frequency of a spring-mass system. I am given the damping constant, the mass of the object at the end of the spring, the mass of the spring, and the spring constant. I know that angular frequency equals the square root of the spring constant over the mass at the end of the spring, but I don't understand how to find the angular frequency now that the spring has a mass. My assumption is that I sum up the mass of the spring and the object at the end of the spring.
 
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  • #3
Ok, I did some research before and found something similar to that, but I wasn't sure if I had to do that.

thanks.
 

1. What is angular frequency in damped oscillation?

Angular frequency in damped oscillation refers to the rate at which a damped oscillating system completes one full cycle of oscillation. It is measured in radians per second and is denoted by the symbol ω.

2. How do you calculate angular frequency in damped oscillation?

The formula for calculating angular frequency in damped oscillation is ω = √(k/m - (b/2m)^2), where k is the spring constant, m is the mass of the oscillating object, and b is the damping coefficient.

3. What is the relationship between angular frequency and damping ratio in damped oscillation?

The damping ratio (ζ) in damped oscillation is directly related to the angular frequency (ω) through the formula ζ = b/2√(km), where b is the damping coefficient, k is the spring constant, and m is the mass of the oscillating object.

4. How does damping affect the angular frequency in damped oscillation?

Damping reduces the angular frequency in damped oscillation. As the damping coefficient increases, the energy dissipated by the system also increases, resulting in a decrease in the amplitude of oscillations and a decrease in the angular frequency.

5. What is the significance of finding the angular frequency in damped oscillation?

Finding the angular frequency in damped oscillation is important as it allows us to understand the behavior of a damped oscillating system. It helps in predicting the amplitude and frequency of oscillations and can be used to design and control damped oscillation systems in various fields such as engineering, physics, and biology.

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