Consider the system shown in Figure 5.74. A uniform solid cylinder of mass (m), radius (R), and

Question:

Consider the system shown in Figure 5.74. A uniform solid cylinder of mass $m$, radius $R$, and length $L$ is fitted with a frictionless axle along the cylinder's long axis. A spring of stiffness $k$ is attached to a bracket connected to the axle. Assume that the cylinder rolls without slipping on a horizontal surface. Draw the necessary free-body diagram and derive the differential equation of motion.

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