Understanding Damping Coefficients in Vibrational Systems

[jrm2002]

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??

 

[mezarashi]

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)

 

[jrm2002]

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?