A five-degree of model of a railroad bridge is shown in Figure P7.85. The bridge is composed of five rigid spans. The connection between each span and its base is modeled as a torsional spring. Using the angular displacements of the spans as the generalized coordinates, derive the differential equations governing the motion of the bridge.

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h FIGURE P7.85 0. m, I 0. m, 1 h m, I