Problem $3(20$ marks$)$

The governing differential equation of the elastic curve for a cantilever beam is given by

$EI\frac{d^{2}y}{d{x}^2}+\frac{w}{2}(L-x{)}^2=0$

Use FDM with $2$ segments $(n=2)$ to compute the displacement $(y)$ and slope $(d\frac{y}{d}x)$ at the free end

of the beam. Take $E=200$GPa,$I=100{10}^{-6}{m}^4.$

Solution