The graph shows the variation of the water level relative to mean sea level in Commencement Bay at Tacoma, Washington, for a particular 24-h period. Assuming that this variation is modeled by simple harmonic motion, find an equation of the form

y = a sin(ωt)

that describes the variation in water level as a function of the number of hours after midnight.

We are given with the simple harmonic motion equation
y = a sin(ωt)
a is the amplitude which can be obtained from getting the highest water level with respect to the mean water level.
ω can be obtained by taking the period of the changing water level. If T is the period then,
ω = 2π / T

Answer Link

AkshayG AkshayG · Answer 2 · 2019-10-25T06:55:58-04:00

The amplitude of the equation is the maximum water level and the value of w is the period of changing water level.

Further explanation:

The function is periodic and the equation can be expressed as follows,

\(\boxed{y = a\times\sin\left( {wt} \right)}\)

Here, a is amplitude of the function, period of the function is \(wt.\)

Given:

The period of the function is 24-h.

Explanation:

The simple harmonic motion equation is given as follows,

\(y = a\times\sin \left( {wt}\right)\)

“a” is the amplitude of the function and can be obtained from the highest level of water in respect of the mean water level.

The value of w can be obtained from the change of water level.

\(w =\dfrac{{2\pi }}{T}\)

The amplitude of the equation is the maximum water level and the value of w is the period of changing water level.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: College

Subject: Mathematics

Chapter:Periodic functions

Keywords: Phase shift, variation, water level, mean sea level, Commencement Bay, Tacoma, Washington, modeled, simple harmonic motion, equation, number of hours, midnight, periodic function, horizontal translation, function, horizontal length, cycle, one cycle of the function, number, vertical translation, amplitude, horizontal unit.