A Spring with A $3 - \mathrm { kg }$ Mass Is Held Stretched

A spring with a $3 - \mathrm { kg }$ mass is held stretched $0.9 \mathrm {~m}$ beyond its natural length by a force of $30 \mathrm {~N}$ . If the spring begins at its equilibrium position but a push gives it an initial velocity of $1 \mathrm {~m} / \mathrm { s }$ , find the position $x ( t )$ of the mass after $t$ seconds.

A) $x ( t ) = 0.3 \sin \left( \frac { 10 } { 3 } t \right)$
B) $x ( t ) = 0.4 \cos \left( \frac { 10 } { 3 } t \right)$
C) $x ( t ) = 1 \sin ( 7 t )$
D) $x ( t ) = 0.3 \sin \left( \frac { 10 } { 3 } t \right) + 0.4 \cos \left( \frac { 10 } { 3 } t \right)$
E) $x ( t ) = \frac { 10 } { 3 } \sin ( 7 t )$

Correct Answer:

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