A Spring with A $16 - \mathrm { kg }$ Mass Has Natural Length

Multiple Choice

A spring with a $16 - \mathrm { kg }$ mass has natural length $0.8 \mathrm {~m}$ and is maintained stretched to a length of $1.2$ $\mathrm { m }$ by a force of $19.6 \mathrm {~N}$ . If the spring is compressed to a length of $0.4 \mathrm {~m}$ and then released with zero velocity, find the position $x ( t )$ of the mass at any time $t$ . Select the correct answer.

A) $x ( t ) = 0.8 \sin ( 1.75 t )$
B) $x ( t ) = - 0.4 \cos ( 1.75 t )$
C) $x ( t ) = - 0.4 e ^ { - 4 t } \cos ( 0.4 t )$
D) $x ( t ) = - 0.4 e ^ { - 4 t } \cos ( 1.75 t )$
E) $x ( t ) = - 0.4 \cos ( 1.75 t ) + 0.4 \sin ( 1.75 t )$