There are 3 unknowns generally in the equation describing SHM.
They are amplitude, frequency & phase constant .
Thus if amplitude , frequency & phase constant.
Thus if three observations displacement are made at three time instants then three simultaneous equations can be set & they can be solved to describe the motion completely.
Note some times the initial displacement & Initial velocity can both can be zero which will result in 4 unknowns.
3 is the right answer.