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.

Question

Twig

Mathematics

7 August, 03:43

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.

+4

Answers (1)

Know the Answer?

Rory Yu · Answer 1

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