Consider the mechanical system shown in Figure 5.91, where the motion of the rod is small angular rotation. When \(\theta=0\) and \(f=0\), the deformation of each spring is zero and the system is at static equilibrium. Assume that the friction between the block of mass \(m_{1}\) and the horizontal surface cannot be ignored and is modeled as a translational viscous damper of damping coefficient \(b\).

a. Assuming that \(a>c>0\), determine the mass moment of inertia of the rod about the pivot point \(\mathrm{O}\).

b. Draw the necessary free-body diagram and the kinematic diagram, and derive the equations of motion for small angles.

Transcribed Image Text:

FIGURE 5.91 Problem 4. a M k 0000 C 0000 m2 m