A 2-Pound Weight Is Hung on a Spring and Stretches $x ( t )$

A 2-pound weight is hung on a spring and stretches it 1/2 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 4 inches from equilibrium and released, the initial value problem describing the position, $x ( t )$ , of the mass at time $t$ is

A) $x ^ { \prime \prime } - 16 x ^ { t } + 64 x = 0 , x ( 0 ) = 4 , x ^ { \prime } ( 0 ) = 0$
B) $x ^ { \prime \prime } + 16 x ^ { t } + 64 x = 0 , x ( 0 ) = 4 , x ^ { \prime } ( 0 ) = 0$
C) $x ^ { \prime \prime } - 16 x ^ { \prime } + 64 x = 0 , x ( 0 ) = 1 / 3 , x ^ { \prime } ( 0 ) = 0$
D) $x ^ { \prime \prime } + 16 x ^ { \prime } + 64 x = 0 , x ( 0 ) = 1 / 3 , x ^ { \prime } ( 0 ) = 0$
E) $x ^ { \prime \prime } + 64 x = 16 , x ( 0 ) = 1 / 3 , x ^ { \prime } ( 0 ) = 0$