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

question 2

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) \(y = \frac { 5 } { 24 } \sin ( 2 t + 0.9273 )\)

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