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

question 30

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) \(E L y ^ { \prime \prime \prime \prime } = w _ { 0 } \delta ( x + L / 2 ) , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 0 , y ^ { \prime \prime } ( L ) = 0 , y ^ { \prime \prime \prime } ( L ) = 0\)

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Definitions:

Environmental Events

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Neuroticism

A personality trait characterized by emotional instability, anxiety, moodiness, worry, and sadness, considered one of the five major traits in the study of personality.

Extraversion

A personality trait characterized by energy, positive emotions, and the tendency to seek stimulation in the company of others.

Fraternal Twins

Siblings born at the same time who have developed from two separate eggs fertilized by different sperm, making them genetically distinct.