2. The deflection of the simply supported beam shown in the figure is assumed as v(x) = cx{x - 1), where c is a constant. A force is applied at the center of the beam. Use the following properties: EI = 1000 N-m2 and L = 1 m. First,

(a) show that the above approximate solution satisfies displacement boundary conditions, and

(b) use Rayleigh-Ritz method to deter¬

mine c.