A Weight Is Attached to a Spring $P ( t ) = 0.5 \sin \left( \pi t + \frac { n } { 2 } \right) + 1.2$

question 25

Essay

A weight is attached to a spring. Suppose the position (in meters) of the weight above the floor t seconds after it is released is given by $P ( t ) = 0.5 \sin \left( \pi t + \frac { n } { 2 } \right) + 1.2$ (a) What is the position of the weight when t = 2? When t = 3? When t = 4?
(b) What is the average rate of change of the position of the weight (in m/s) over the time interval [2, 4]? Over the time interval [2, 3]?
(c) The average rate of change of the position of the weight over the time period [2; 6] is 0. Does this mean that the weight has come to a stop? Why or why not?

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Definitions:

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The Occupational Safety and Health Administration, a U.S. government agency responsible for ensuring safe and healthful working conditions by setting and enforcing standards.

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