Damping

Any real vibrating system tends to lose mechanical energy as a result of friction and other loss mechanisms.

Damping of an oscillating system corresponds to a loss of energy or equivalently, a decrease in the amplitude of vibration.

Figure 23: A mass-spring-damper system.

The drag force $F_r$ is proportional to the velocity and is given by

$$F_r = -Rv \qquad \longrightarrow \qquad F_r = -R\frac{dx}{dt}$$

where $R$ is the mechanical resistance.