A Spring with A $16$ -Kg Mass Has Natural Length $0.8$ M and Is Maintained Stretched to a Length Of

question 1

Multiple Choice

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

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