Use the free-body diagram method to derive the differential equations governing the motion of the systems shown in Figure P7.5 using the indicated generalized coordinates. Make linearizing assumptions and write the resulting equations in matrix form.

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0.1L 0.41 0.31 G 2k -0.2L x1 m2 FIGURE P7.5 1X2 2k Rod of mass m moment of inertia I