Suppose a 32-Pound Weight Is Suspended on a Spring $\frac { 1 } { 3 } \text { foot }$

question 32

Multiple Choice

Suppose a 32-pound weight is suspended on a spring. The weight is pulled $\frac { 1 } { 3 } \text { foot }$ below the equilibrium position and released. The motion takes place in a Med that furnishes a damping force of magnitude $\frac { 1 } { 8 }$ speed at all times. Assume that the weight stretches the spring $\frac { 2 } { 3 }$ foot from its natural position. Find a formula for the position of the weight as a function of time $t$ .

• A) \(y ( t ) = 3 \left( \cos \frac { \sqrt { 12,287 } t } { 16 } + \frac { \sqrt { 12,287 } } { 12,287 } \sin \frac { \sqrt { 12,287 } t } { 16 } \right)\)
• B) \(y ( t ) = \frac { e ^ { - t / 16 } } { 12 } \left( \cos \frac { \sqrt { 12,287 } t } { 16 } + \frac { \sqrt { 12,287 } } { 12,287 } \sin \frac { \sqrt { 12,287 } t } { 16 } \right)\)
• C) \(y ( t ) = \frac { e ^ { - t / 16 } } { 3 } \left( \cos \frac { \sqrt { 12,287 } t } { 16 } + \frac { \sqrt { 12,287 } } { 12,287 } \sin \frac { \sqrt { 12,287 } t } { 16 } \right)\)
• D)\(y ( t ) = 6 \left( \cos \frac { \sqrt { 12,287 } t } { 16 } + \frac { \sqrt { 12,287 } } { 12,287 } \sin \frac { \sqrt { 12,287 } t } { 16 } \right)\)
• E)\(y ( t ) = \left( \cos \frac { \sqrt { 12,287 } t } { 16 } + \frac { \sqrt { 12,287 } } { 12,287 } \sin \frac { \sqrt { 12,287 } t } { 16 } \right)\)

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Definitions:

Collectivism

A cultural value that emphasizes the importance of groups and the collective over the individual, promoting interdependence and cooperation.

Reciprocal Determinism

A psychological principle indicating that an individual's actions are simultaneously shaped by and shape their own characteristics and the surrounding milieu.

Self-serving Bias

The common tendency to attribute positive events to one's own character but attribute negative events to external factors.

Self-esteem

An individual's subjective evaluation of their own worth, encompassing beliefs about oneself as well as emotional states.