y(t) = a sin(ωt).
The graph of the motion starts at y-0 t = 0 so we use sine in the equation
y(t) = A sin (2π t / T) where A = the amplitude and T = the period so here we can write:
Displacement at t = y(t) = a sin(2π/ 2π/ω)t
y(t) = a sin(ωt)