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

question 30

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) . Find the amplitude of the oscillations of the weight.
​

• A) \(\frac { 1 } { 24 } \mathrm { ft }\)
• B) \(\frac { 1 } { 10 } \mathrm { ft }\)
• C) \(\frac { 5 } { 24 } \mathrm { ft }\)
• D) \(\frac { 1 } { 5 } \mathrm { ft }\)
• E) \(\frac { 24 } { 5 } \mathrm { ft }\)

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Definitions:

Production Possibilities Frontier

A curve depicting all maximum output possibilities for two goods, given a set of inputs, representing the trade-offs of allocating resources between the production of those goods.

Opportunity Cost

The act of losing potential gains by not exploring other alternatives and choosing one.

Production Possibilities

This represents a diagram that outlines the peak production options for two different goods, taking into account a mixture of inputs such as resources and other variables.

Production Possibilities Frontier

A curve depicting all maximum output possibilities for two or more goods, given a set of inputs, representing the trade-offs in production choices.