Consider a system consisting of discrete masses connected by springs in series as shown in Figure 7.41. Derive the equation of motion for mass \(m_{i}\) using Newton's second law, arrange the equation in incremental form, take the limit, and derive the differential equation of motion for the longitudinal vibration of a thin beam.

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14-1 www mm k www. www m m-1 + AX-1 Ar Figure 7.41: Discrete mass-spring system constrained to move horizontally.