PROBLEMS 1) Use Lagrange's equations to derive the differential equations governing the motion of the system of Fig. 1 using x and x2 as generalized coordinates. Express the equations in matrix form. mm m x1 HE X2 m 2c E Fig. 1 2) Use Lagrange's equations to derive the differential equations governing the motion of the system of Fig. 2 using x and x2 as generalized coordinates. Express the equations in matrix form. (Note: The roller rolls without slip). x1. x2 5 k₁ mmm k2 m1 02 01 m2.Jo Fig. 2 3) Use Lagrange's equations to derive the differential equations governing the motion of the system of Fig. 3 using 61, 62 and x as generalized coordinates. Express the equations in matrix form. 2r 3k 00000 2r 12 eeeee k Fig. 3 m x