For the mechanical system in Problem 2, use the energy method to derive the equation of motion.

The double pulley system shown in Figure 5.89 has an inner radius of \(r_{1}\) and an outer radius of \(r_{2}\). The mass moment of inertia of the pulley about point \(\mathrm{O}\) is \(I_{\mathrm{O}}\). A translational spring of stiffness \(k\) and a block of mass \(m\) are suspended by cables wrapped around the pulley, as shown. Draw the free-body diagram and kinematic diagram, and derive the equation of motion by using the force/moment approach.

Transcribed Image Text:

FIGURE 5.89 Problem 2. m elle