Problem $2.[5]$ A cantilever beam, with elastic modulus $\backslash (($E$)\backslash ),$ second moment of area $($I$)$ and length $($L$),$ is subject to a uniformly distributed load $(\backslash ($ w $\backslash ))$ with an end point load $\backslash (($P$)\backslash )$ and fixed end moment $($M$).$ Determine

a$)$ the exact analytical solution for the deflection, moment and shear force along the beam length, and

b$)$ using a cubic polynomial displacement field, compare the Rayleigh Ritz solution with the exact analytical solution. Check your solution with the boundary conditions and ordinary differential equation of motion.