Use Lagrange's equations to derive the differential equations governing the motion of the systems shown in Figures P7.3. Use the indicated generalized coordinates. Make linearizing assumptions, and write the resulting equations in matrix form. Indicate whether the system is statically coupled, dynamically coupled, neither, or both.

FIGURE P7.3 L/4 L/4 k Slender rod of mass m 2k m 2m X2