Solve the Problem $$P = 4 \cos ( 4 t )$$

question 94

Essay

Solve the problem.
-A mass hangs from a spring which oscillates up and down. The position P (in feet) of the mass at time t (in seconds) is
given by $$P = 4 \cos ( 4 t )$$
For what values of $t , 0 \leq t < \pi$ , will the position be $2 \sqrt { 2 }$ feet? Find the exact values. Do not use a calculator.

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Definitions:

F-test

A statistical procedure that compares the variances between two samples to assess if they originate from populations with identical variances.

Random Variable

A variable that takes on various numerical values, each associated with a certain probability, representing outcomes of a random phenomenon.

Within-treatments Variation

Variability observed within groups in an experiment, indicating how much participants in the same group differ from each other.

Sum of Squares

The total of the squared differences between each observation and the mean of the data set, used in statistical analyses to measure variance.