Solve the problem.
-The position of a weight attached to a spring is $s ( t ) = - 5 \cos 16 \pi t$ inches after $t$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height?
A) The maximum height of 5 inches is first reached after $0.06$ seconds.
B) The maximum height of 10 inches is first reached after 4 seconds.
C) The maximum height of 5 inches is first reached after 8 seconds.
D) The maximum height of 10 inches is first reached after 8 seconds.

Question

Quizplus · Accepted Answer

The maximum height is determined by the amplitude of the cosine function, which is 5 inches. The first maximum occurs at $t = \frac{1}{4} \times \frac{1}{16} = \frac{1}{64}$ seconds, which is approximately 0.015625 seconds, but none of the options exactly match this calculation. Option A is the closest to the correct timing and accurately reflects the maximum height.

Solve the Problem s(t)=−5cos⁡16πts ( t ) = - 5 \cos 16 \pi ts(t)=−5cos16πt

Solve the Problem $s ( t ) = - 5 \cos 16 \pi t$