3. Use the Rayleigh-Ritz method to determine the deflection v(x), bending moment M(x), and shear force Vy{x) for the beam shown in the figure. The bending moment and shear force are calculated from the deflection as M(x) = EId2v/dx2 and Vy{x) = -EltPv/dx?. Assume the dis¬

placement as v(x) = eg + c\x + C2X2 + C3X3, and £7= 1,000N-m2, L = 1 m, and po—

100 N/m, and C = 100 N-m. Make sure that the displacement boundary conditions are satisfied a priori.

Hint: Potential energy of a couple is calculated as V = —Cdv/dx, where the rotation is calcu¬

lated at the point of application of the couple.