The x-t equation of a particle moving along x-axis is given by x= A+ A [1-cos $\omega$ t], then the 

$x=2A-A\cos wt$

At t=0, it is left extreme and momentarily at rest and this, point is x= A. Its amplitude is A. So the particle oscillates between x= +A to x= +3A x= 2 A being  its mean position.

$\begin{array}{l}T=2\pi /3\Rightarrow t_{Ato3A}=T/2=\pi /w\\ Also{t}_{Ato2A}\frac{T}{4}=\frac{\pi }{2w}\end{array}$