Consider the Problem of a Vibrating String, Tightly-Stretched Between $x = 0$

question 21

Multiple Choice

Consider the problem of a vibrating string, tightly-stretched between $x = 0$ and $x = 1$ , with a fixed initial position, $f ( x )$ , and zero initial velocity. The mathematical problem for the deflection, $u ( x , t )$ , is $( \text { with } u ( 0 , t ) = 0 , u ( 1 , t ) = 0 )$

• A) \(\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial u } { \partial t } , u ( x , 0 ) = f ( x ) , u _ { t } ( x , 0 ) = 0\)
• B) \(\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial u } { \partial t } = 0 , u ( x , 0 ) = f ( x ) , u _ { t } ( x , 0 ) = 0\)
• C) \(\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } , u ( x , 0 ) = f ( x ) , u _ { t } ( x , 0 ) = 0\)
• D) \(\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } + \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } = 0 , u ( x , 0 ) = f ( x ) , u _ { t } ( x , 0 ) = 0\)
• E) \(\frac { \partial ^ { 2 } u } { \partial x ^ { 2 } } = \frac { \partial ^ { 2 } u } { \partial t ^ { 2 } } , u ( x , 0 ) = 0 , u _ { t } ( x , 0 ) = f ( x )\)