The system shown in Fig. 2.2 consists of a rope of initial length L under tension T and subjected to a transverse force f(x) (Figure 2.2). T w(x) T L f(x) Figure 2.2 Assuming that the deflection w(x) is small and that the tension T is constant, the expression of the potential energy for this system can be shown to be 1 L 2 - " T (du) dr- f f(x)\w(x)dr 'dw dx Using the variational method (i.e., using the PMPE), derive the expression for the local stiffness matrix [k] and the local load vector {r} for a 2-node and a 3-node "generic rope element" of length . For the local load vector, assume that the applied load f(x) constant (fo) on the element.