A 4-Pound Weight Is Hung on a Spring and Stretches $x ( t )$

Multiple Choice

A 4-pound weight is hung on a spring and stretches it 1 foot. The mass spring system is then put into motion in a medium offering a damping force numerically equal to the velocity. If the mass is pulled down 6 inches from equilibrium and released, the initial value problem describing the position, $x ( t )$ , of the mass at time t is

A) $x ^ { \prime \prime } - 8 x ^ { \prime } + 32 x = 0 , x ( 0 ) = 6 , x ^ { \prime } ( 0 ) = 0$
B) $x ^ { \prime \prime } + 8 x ^ { \prime } + 32 x = 0 , x ( 0 ) = 6 , x ^ { \prime } ( 0 ) = 0$
C) $x ^ { \prime \prime } - 8 x ^ { \prime } + 32 x = 0 , x ( 0 ) = 1 / 2 , x ^ { \prime } ( 0 ) = 0$
D) $x ^ { \prime \prime } + 8 x ^ { \prime } + 32 x = 0 , x ( 0 ) = 1 / 2 , x ^ { \prime } ( 0 ) = 0$
E) $x ^ { \prime \prime } + 32 x = 8 , x ( 0 ) = 1 / 2 , x ^ { \prime } ( 0 ) = 0$