This is not really a trig question. It is an understanding question.
dH/dt will be 0 when the tangent to the circle is horizontal. That is at the top and bottom. (say 12oclock and 6oclock)
If is starts horizontal to the axis that is at 3oclock or 9 oclock.
So it must travel a quarter of a rotation to get to the top or the bottom,
45/4 = 11.25 seconds then again at 11.25+22.5k seconds (where k is a positive integer)