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

question 25

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) .
$y = \frac { 1 } { 8 } \sin 2 t + \frac { 1 } { 6 } \cos 2 t$
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) \(y = \frac { 5 } { 24 } \sin ( 2 t + 0.9273 )\)
• 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) \(y = \sin ( 2 t + 0.9273 )\)

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Definitions:

Market Price

The market price at which you can currently buy or sell a service or asset.

Efficient Equilibrium

A state in an economy where every resource is optimally allocated to serve each individual or entity in the best way while minimizing waste and inefficiency.

External Benefits

Benefits resulting from a transaction that affect parties not directly involved in the transaction, often leading to positive outcomes for society.

External Costs

Costs of a transaction or activity that affect third parties who did not choose to incur that cost, often seen in environmental pollution.