A Weight Is Attached to a Spring Suspended Vertically from a Ceiling.When

Multiple Choice

A weight is attached to a spring suspended vertically from a ceiling.When a driving force is applied to the system, the weight moves vertically from its equilibrium position, and this motion is modeled by
$y = \frac { 1 } { 8 } \sin 2 t + \frac { 1 } { 6 } \cos 2 t$
Where y is the distance from equilibrium (in feet) and t is the time (in seconds) .

Use the identity $a \sin B \theta + b \cos B \theta = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B \theta + C )$ where $C = \arctan ( b / a ) , a > 0$ , to write the model in the form $y = \sqrt { a ^ { 2 } + b ^ { 2 } } \sin ( B t + C )$ .

A) $y = \sin ( 2 t + 0.9273 )$
B) $y = \frac { 24 } { 5 } \sin ( 2 t + 0.9273 )$
C) $y = \frac { 24 } { 5 } \sin ( 2 t - 0.9273 )$
D) $y = \sin ( 2 t - 0.9273 )$
E) $y = \frac { 5 } { 24 } \sin ( 2 t + 0.9273 )$