A rotor of mass \(m\) is mounted on an elastic shaft with journal bearings at both ends. A three degree-of-freedom model of the system is shown in Figure P7.83. Each journal bearing is modeled as a spring in parallel with a viscous damper. Drive the differential equations governing the transverse motion of the system.

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L/2 m JC E, I m Tx FIGURE P7.83 L/2 m X3