For the system in Figure 5.49, the inputs are the forces \(f_{1}\) and \(f_{2}\) applied to the masses and the outputs are the displacements \(x_{1}\) and \(x_{2}\) of the masses.

a. Draw the necessary free-body diagrams and derive the differential equations of motion.

b. Write the differential equations of motion in the second-order matrix form.

c. Using the differential equations obtained in Part (a), determine the state-space representation.

Transcribed Image Text:

2x- Y < D b m2 elle k mi elle elle FIGURE 5.49 Problem 14.