The restoring force in a vibrating system may be provided by a real physical spring (say a close coiled helical spring or a leaf spring in an automobile suspension) or by an “effective” spring action. For example in the case of the to-and-fro oscillations of a simple pendulum, the restoring force is actually provided by gravity. It is the weight of the bob that tends to bring it back to its original equilibrium position and thus gravity acts as the effective spring here. There could also be electro-magnetic or such other forces that provide the restoring action. We will consider all of these under the head, springiness in the system.

Dissipation in a system is perhaps the hardest to model mathematically in accurate manner, simply because there can be many sources of damping involving complex physical phenomena. For example, automobile shock absorbers have piston-cylinder kind of fluid friction based dampers normally referred to as viscous dampers. There can also be contact friction between two mating surfaces (such as piston-cylinder interface; cam-follower etc) which is normally considered to be of Coulombic type. Additionally there can be material internal friction (hysteresis) damping. Considering all such various sources of damping present in a system and developing accurate mathematical models for the same is a challenging task. Often, total energy being dissipated is approximately modeled using a simple linear viscous damper.

We will discuss the fourth element of a typical vibrating system namely the external disturbance in the next lecture.