Example

Consider a two DOF vibrating system supported on friction-less wheels as shown in Fig. 24.1. Obtain the state space representation of the system.

Figure 24.1: 2 DOF vibration system

Solution The equation of motion of the 2 DOF system may be written as:

	(24.2)

Consider the state vector x as:

Eqn 24.2 could be expressed as a set of four first order ODEs with respect to the above state vector. The ODEs could be written as:

	(24.3)

The output measured by the sensors may vary from case to case. For example, considering a case, where, velocity of the first mass and the relative displacement between the two masses (x₁– x₂ ) are only measurable. The equations could be now expressed in matrix-form resembling Eqn. (24.1) as

(24.4)