Sorry - I looked at this earlier, but had to go. Here's how to fix things, if you haven't already done so.

Question

Your function 10-8cos(0.4t) has the correct period, but is a minimum at t=0. Part (c) of this problem indicates you want to be at axle height when t=0.
That would be 10+8sin(0.4t), which starts at the center, and rises.
But, since cos(x) = sin(π/2 -x) you want
h(t) = 10 - 8cos(π/2 - 0.4t) = 10 - 8cos(0.4 (π/5 - t))
or, since cos(-x) = cos(x), it might look nicer as
h(t) = 10 - 8cos(0.4 (t - π/5))
That also helps to show the shift of 1/4 period.