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

question 16

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 where is the distance from equilibrium (in feet) and is the time (in seconds) . $y = \frac { 1 } { 4 } \sin 2 t + \frac { 1 } { 3 } \cos 2 t$ 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) \(\quad y = \sin ( 2 t - 0.9273 )\)
• B) \(y = \sin ( 2 t + 0.9273 )\)
• C) \(y = \frac { 12 } { 5 } \sin ( 2 t - 0.9273 )\)
• D) \(y = \frac { 5 } { 12 } \sin ( 2 t + 0.9273 )\)
• E) \(y = \frac { 12 } { 5 } \sin ( 2 t + 0.9273 )\)

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Definitions:

Reducing Sugars

Sugars capable of acting as reducing agents, having free aldehyde or ketone groups that allow them to reduce other compounds, commonly tested by Benedict's or Fehling's solution.

Ketose

A type of monosaccharide (simple sugar) where the carbonyl group is a ketone, found in several biochemical pathways.

Aldose

A type of carbohydrate that contains an aldehyde group as its carbonyl functional group.

Glycosides

Compounds formed from a sugar and another compound by replacement of a hydroxyl group in the sugar by another group.