A Uniform Beam of Length L Has a Concentrated Load $w _ { 0 }$

Multiple Choice

A uniform beam of length L has a concentrated load, $w _ { 0 }$ , at $x = L / 2$ . It is embedded at the left end and free at the right end. The correct initial value problem for the vertical deflection, $y ( x )$ , at a distance x from the embedded end is

A) $E L y ^ { \prime \prime \prime \prime } = w _ { 0 } \delta ( x - L / 2 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ^ { \prime \prime } ( L ) = 0 , y ^ { \prime \prime \prime } ( L ) = 0$
B) $y ^ { \prime \prime \prime \prime } = E I w _ { 0 } \delta ( x - L / 2 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ^ { \prime \prime } ( L ) = 0 , y ^ { \prime \prime \prime } ( L ) = 0$
C) $E L y ^ { \prime \prime } = w _ { 0 } \delta ( x - L / 2 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ^ { \prime \prime } ( L ) = 0 , y ^ { \prime \prime \prime } ( L ) = 0$
D) $y ^ { \prime \prime } = E I w _ { 0 } \delta ( x - L / 2 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ^ { \prime \prime } ( L ) = 0 , y ^ { \prime \prime \prime } ( L ) = 0$
E) $E L y ^ { \prime \prime \prime \prime } = w _ { 0 } \delta ( x + L / 2 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ^ { \prime \prime } ( L ) = 0 , y ^ { \prime \prime \prime } ( L ) = 0$