Determine the equation of the graph.
-The position of a weight attached to a spring is $\mathrm { s } ( \mathrm { t } ) = - 5 \cos 8 \pi t$ inches after $\mathrm { t }$ seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height? Round values to two decimal places, if necessary.
A) The maximum height of 5 inches is first reached after $0.13$ seconds.
B) The maximum height of 10 inches is first reached after 2 seconds.
C) The maximum height of 10 inches is first reached after 4 seconds.
D) The maximum height of 5 inches is first reached after 4 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 $t = \frac{1}{16}$ seconds, which rounds to 0.06 seconds, not 0.13. However, given the options, A is the closest to the correct timing despite the rounding error.

Determine the Equation of the Graph s(t)=−5cos⁡8πt\mathrm { s } ( \mathrm { t } ) = - 5 \cos 8 \pi ts(t)=−5cos8πt

Determine the Equation of the Graph $\mathrm { s } ( \mathrm { t } ) = - 5 \cos 8 \pi t$