If the damper is present in the system, the vibrations are said to be damped vibrations. Damped vibrations can be free vibrations or forced vibrations. we are going to study the damped free vibrations.
TYPES OF DAMPING:
1] Viscous damping:
This type of damping occurs in lubricated sliding surfaces, where there is a smaller relative velocity. for viscous dampers, the damping resistance is always proportional to the relative velocity.
There are two important types of viscous dampers:
a] Fluid dash pot.
b] Eddy current damping.
2] Dry friction of coulomb damping:
This type of damping occurs when two machine parts rub against each other, dry or unlubricated. The damping resistance in this case is practically constant and is independent of the rubbing velocity, when two dry surfaces rub against each other, then a frictional force 'F' is acted upon, which is proportional to be normal reaction, $R_N$ between the two mating parts.
Let $\mu$ = co-efficient of friction,
then $F = \mu R_N$
and $\mu$ will be constant throughout the velocity range of dry frictions.