Question

I’m your research, you model the waves as being driven by sinusoids source with a frequency of 0.267Hz with the magnitude of the vertical displacement between the crest of one wave and the trough/valley of another is 6.00m. The vertical displacement is symmetric about the origin in the y-dimension. The speed of the waves passing your testing location is 5.30m/s and the waves are moving toward shore. At t=0, a wave crest, at its maximum vertical displacement, passes your testing equipment at your research location.
A. Write out the time and position dependent mathematical equation that describes the waves moving past your testing equipment (no number just variables).

B. What is the magnitude of the amplitude A, angular frequency omega, period T, wavelength, and wave number k describing the waves in your surrounding research location under these conditions? You are significantly far from shore;assume no waves bounce back from shore.
C. Write out the time and position dependent mathematical equation that describes the velocity and the acceleration past the test equipment bobbing up and down in the ocean as the waves move past your testing equipment.

D. Given the above conditions, which remain constant, what is the mathematical equation that describes the vertical position as a function of time only of your neighboring testing equipment located 1609m away from your original testing location closer toward shore.

Answer 1

A. The equation for the waves moving past the equipment, considering that the waves move towards the testing location, and that at t=0s, the vertical displacement is maximum there, is given by:

B. The requested parameters are:

If we plug this values:

C. The velocity and acceleration equations can be found deriving the position equation:

D. The equation that describes the vertical position as a function of time at a point 1609m away from the testing location is: