Viscously damped free vibration :

Viscous damping force is expressed as,

                                                                                                                                             (3.16)

c is the constant of proportionality and it is called damping co-efficient.

Figure 3.2 shows spring-damper-mass system with free body diagram.

From free body diagram, we have

                                                                                                                                                    (3.17)

            

                                                                                                                               (3.18)