$1.)$ Determine the maximum deflection $$ in a simply supported beam of length $L=4m$ carrying a concentrated load $P=20N$ at midspan. Use $G=10$GPa, and $I=1\mathrm{.}5{10}^{-7}{m}^4.$

$2.)$ Determine the maximum deflection $$ in a simply supported beam of length $L=4m$ carrying a uniformly load of intensity $w=5\frac{N}{m}$ applied over its entire length. Use $G=10$GPa, and $I=1\mathrm{.}5{10}^{-7}{m}^4.$

Provide a detailed solution.