Consider the two-degree-of-freedom mass-spring system as shown in Figure 10.85, in which two masses are to be controlled by two equal and opposite forces \(f\). The equations of motion of the system are derived as

\[\begin{gathered}m \ddot{x}_{1}+2 k x_{1}-k x_{2}=f \\m \ddot{x}_{2}-k x_{1}+2 k x_{2}=-f\end{gathered}\]

Show that the system is uncontrollable. Using the concept of mode discussed in Section 9.4, associate a physical meaning with the controllable and uncontrollable modes.

Transcribed Image Text:

FIGURE 10.85 Problem 4. -x2 k 0000 m 0000 m