Equations (8.4) and (8.5) can be combined (eliminating t) to give

	(8.6)

This equation suggests that the plot of versus over a cycle generates an ellipse, as shown in Fig. 8.2, with and , respectively, as the semi-major and minor axes.

Figure 8.2: Damping force profile

The area of this ellipse signifies the energy dissipation per cycle, which again, is

i.e., the same as given by eqn.(8.6).

Figure 8.3: Energy dissipation

If the combined stiffness and damping of a vibrating system is modelled as an ideal linear spring and a viscous dashpot in parallel (Fig. 8.4a), then, for a harmonic displacement, the force displacement characteristic for every cycle is obviously an elliptic loop as indicated in Fig. 8.3b. This model, known as the Kelvin-Voigt model, is commonly used to represent a real-life system.

Congratulations! You have finished module 2.