The Initial Value Problem $( L - x ) \frac { d ^ { 2 } x } { d t ^ { 2 } } - \left( \frac { d x } { d t } \right) ^ { 2 } = L g , x ( 0 ) = 0 , x ^ { \prime } ( 0 ) = 0$

question 26

Multiple Choice

The initial value problem $( L - x ) \frac { d ^ { 2 } x } { d t ^ { 2 } } - \left( \frac { d x } { d t } \right) ^ { 2 } = L g , x ( 0 ) = 0 , x ^ { \prime } ( 0 ) = 0$ is a model of a chain of length $L$ falling to the ground, where $x ( t )$ represents the length of chain on the ground at time $t$ . The solution for $v = \frac { d x } { d t }$ in terms of $x$ is

• A) \(v = \sqrt { L g \left( L ^ { 2 } - ( L - x ) ^ { 2 } \right) }\)
• B) \(v = \left( \operatorname { Lg } \left( L ^ { 2 } + ( L - x ) ^ { 2 } \right) \right) / ( L - x )\)
• C) \(v = \left( \operatorname { Lg } \left( L ^ { 2 } - ( L - x ) ^ { 2 } \right) \right) / ( L - x )\)
• D) \(v = \sqrt { L g \left( L ^ { 2 } + ( L - x ) ^ { 2 } \right) } / ( L - x )\)
• E) \(v = \sqrt { L g \left( L ^ { 2 } - ( L - x ) ^ { 2 } \right) } / ( L - x )\)

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Definitions:

Animism

A belief that objects, places, and creatures all possess a distinct spiritual essence.

Natural Objects

Items found in nature that are not altered, processed, or created by humans.

Human-like

Exhibiting characteristics, qualities, or behaviors that resemble or mimic those of humans, often used to describe robots or animals.

Egocentrism

Describes the inability to differentiate between one's own perspective and someone else's perspective, often observed in early childhood development.