The solution of the boundary value problem in the previous problem is
A) $y = \omega _ { 0 } / E I \left( L ^ { 3 } x / 48 - L x ^ { 3 } / 16 + x ^ { 4 } / 24 \right)$
B) $y = \omega _ { 0 } / E I \left( x ^ { 2 } / 2 - L x \right)$
C) $y = \omega _ { 0 } E I \left( L ^ { 3 } x / 48 - L x ^ { 3 } / 16 + x ^ { 4 } / 24 \right)$
D) $y = \omega _ { 0 } E I \left( x ^ { 2 } / 2 - L x \right)$
E) none of the above

Question

Quizplus · Accepted Answer

The correct solution to a boundary value problem involving beam deflection under a uniform load $\omega_0$ typically involves terms that account for the beam's length $L$, the position along the beam $x$, and the beam's flexural rigidity $EI$. The expression $y = \omega _ { 0 } / E I \left( L ^ { 3 } x / 48 - L x ^ { 3 } / 16 + x ^ { 4 } / 24 \right)$ correctly incorporates these factors and reflects the form of the solution to the differential equation governing beam deflection, making it the correct choice.

The Solution of the Boundary Value Problem in the Previous y=ω0/EI(L3x/48−Lx3/16+x4/24)y = \omega _ { 0 } / E I \left( L ^ { 3 } x / 48 - L x ^ { 3 } / 16 + x ^ { 4 } / 24 \right)y=ω0​/EI(L3x/48−Lx3/16+x4/24)

The Solution of the Boundary Value Problem in the Previous $y = \omega _ { 0 } / E I \left( L ^ { 3 } x / 48 - L x ^ { 3 } / 16 + x ^ { 4 } / 24 \right)$