Answer
(a) is a sine or cosine function.
Work Step by Step
The equation of motion of an object is :-
$y(t)=+/- Asin(2\times pi\times ft)$
$y(t)$ being the position, A the amplitude, f the frequency of oscillation, and +/- represents the initial upward motion from y(0)=0.
The equation of motion having $90^{\circ}$ phase difference with that of above is :-
$y(t)=+/-Acos(2\times pi \times ft)$
So the equation of motion of a particle in simple harmonic motion is either sine or cosine function of time t with frequency f.
