What's the "cause" of damping coeff. in springs?
Air resistance, friction?
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Friction. More specifically, internal friction (as opposed to air friction) due to the resisting motion between the elements of which the spring is made when the spring undergoes deformation (extension and compression).
When a mass oscillates on an ideal spring (a spring with no internal friction) and in the absence of air friction, the total mechanical kinetic and potential energy of the system is conserved and the oscillation could theoretically go on forever. However, there is always internal friction which dissipates a fraction of the total energy during each oscillation, thereby reducing, or "damping" the oscillation over time until the mass eventually comes to a stop.
Of course air friction can also cause the mass to eventually stop. But this is not related to the damping coefficient.
Hope this helps.