Trigonometric Functions with Periodic Phenomena

Correction to a mis-type on my answer....the function should be :

h(t)  = 3sin [ (pi/8)t - pi/2 ] + 5

And,of course, the amplitude is 3, not 4......!!!!!

Ok so the height varies between 2 and 8 feet, so the amplitude is the heighest point minus the lowest, so the amplitude is 6ft. Your period is 16hrs as long as your x axis is in terms of time, and the midline would be y= the midpoint of the min and max height, which in this case is 3ft.

A possible function is given by :

h(t)  = 4sin [ (pi/8)t - pi/2 ] + 5

The amplitude is 4, the period is 16 radians  ....[ 1 rad  = 1 hour]

The midline is given by :

h(t)   = 5

Here's the graph of both functions :   https://www.desmos.com/calculator/ic00n0hnlr