Understanding Damping Coefficients in Vibrational Systems

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In summary, the conversation discusses the concept of damping forces in a simple pendulum and how they contribute to the reduction of amplitude and eventually the stopping of the pendulum's motion. The damping force is directly proportional to the velocity of vibration, which can be explained by exchanges in momentum between the mass and air molecules. The damping coefficient is a relationship between two quantities and is used to measure the effect of damping forces on the pendulum's motion. It is dependent on the system, including factors such as the material of the pendulum and other properties of the system.
  • #1
jrm2002
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Let us say we have a have mass concentrated at the end of a string(simple pendulum).Let us say the pendlum is set in motion and then eventually due to energy loss through air resistance, the amplitude of the oscillation will reduce and eventually the pendulum comes to rest.

These damping forces are taken in problems as:

Damping force=(Damping Coefficient) x velocity of vibration

My questions are:
1. how is the damping force proportional to velocity of vibration?
2. What is this damping coefficient?What does the damping coefficient physically denote??
 
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  • #2
1. If you could imagine the "damping force" to be caused by exchanges in momentum between the mass and air molecules, it can be seen that the faster the velocity, the more exchanges the mass is making between any particular time interval. Since change in momentum is related to force (see thrust), we get a "damping force".

2. As with any coefficient, the damping coefficient is a relationship between two quantities in which we know the relationship between (i.e. linear, square, exponential, etc). It is also there to remedy our somewhat arbitrary choice of units. For example in the equation F = ma, the mass (in kg) can be thought of as the magical number to relate the acceleration (in m/s) of any object to the force (in Newtons) applied to that object. In this case however, the coefficient appears to physically exist.

And like the F=ma equation (which has the coefficient m dependant on the mass in question), the damping coefficient also depends on the system, just like the coefficient of friction. (i.e. surface area, air density, etc)
 
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  • #3
Thanks for the reply---In the second point you said:
The damping coefficient depends on the system---
Would that incude the material of which the body is made of too?
What properties of the system would the damping coefficient depend upon?
 

1. What is free vibration-damping?

Free vibration-damping refers to the natural oscillation or movement of a structure or system without any external forces applied, and the reduction of that movement through the use of damping materials or techniques.

2. Why is free vibration-damping important?

Free vibration-damping is important because it can help prevent damage to structures or systems caused by excessive or uncontrolled oscillations. It can also improve the performance and stability of a structure or system.

3. What are some common damping materials used in free vibration-damping?

Some common damping materials used in free vibration-damping include rubber, foam, cork, and viscoelastic materials. These materials are often used in the form of coatings, inserts, or layers to absorb and dissipate energy from the vibrating structure or system.

4. How does free vibration-damping work?

Free vibration-damping works by converting the kinetic energy of the vibrating structure or system into heat energy through the use of damping materials. This reduces the amplitude or intensity of the vibration, resulting in less movement and potential damage.

5. Can free vibration-damping be used in all types of structures?

Yes, free vibration-damping can be used in a wide range of structures, including buildings, bridges, vehicles, and industrial equipment. It is particularly useful in structures that are subject to repetitive or high-frequency vibrations, such as wind turbines or aircraft wings.

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