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Oscillations

# How many minimum observations of the displacement (at various time instants) are required to be made to quantify a simple harmonic motion (form the exact equation describing the displacement as a function of time):

$\begin{array}{1 1}(a)\;1 &(b)\;3 \\( c)\; 2 &(d)\;6 \end{array}$

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.