b
Time for $x=0$ to $x=\frac{A}{2}$ is
$\frac{\mathrm{A}}{2}=\mathrm{A} \sin \omega \mathrm{t}_{1} \quad \Rightarrow \omega \mathrm{t}_{1}=\frac{\pi}{6} \Rightarrow \mathrm{t}_{1}=\frac{\pi}{6 \omega}$
$\Rightarrow t_{1}=\frac{T}{12}$
and from $x=\frac{A}{2}$ to $x=A$ is
$\mathrm{t}_{2}=\frac{\mathrm{T}}{4}-\frac{\mathrm{T}}{12}=\frac{\mathrm{T}}{6} \Rightarrow \frac{\mathrm{t}_{1}}{\mathrm{t}_{2}}=\frac{1}{2}$