First of all, what is your question?
I will assume that you want a sinusoidal equation.
I am with you on the amplitude and period of the function.
so let it be F = 300sin(5pi/11)t
This will give us the general shape, all we have to do is to move it up and either left or right to fit the data
as it stands the max is 300 but we want our max to be 800, so let's move it up 500 to get
F = 300sin(5pi/11)t + 500
As it stands we will have a max at 1.1 (a quarter of our period of 4.4), but we want our max to be at 5.1. So we will have to move our curve from above 4 units to the right, which will give us
F = 300sin(5pi/11)(t-4) + 500
let's test it:
if t = 2.9
F = 300sin(5pi/10)(-1.1) + 500 = 200 ..... Check!
if t=5.1
F = 300sin(5pi/10)(1.1) + 500 = 800 .... Check!!!!
so
F = 300sin(5pi/11)(t-4) + 500