Answer
$$=8.3 \times 10^{10} \mathrm{s} \approx 2.6 \times 10^{3} \text { years }
$$
Work Step by Step
We solve $\omega=\omega_{0}+\alpha t$ for the time $t$ when $\omega=0$ :
$$
t=-\frac{\omega_{0}}{\alpha}=-\frac{2 \pi}{\alpha T}$$
$$=-\frac{2 \pi}{\left(-2.3 \times 10^{-9} \mathrm{rad} / \mathrm{s}^{2}\right)(0.033 \mathrm{s})}$$
$$=8.3 \times 10^{10} \mathrm{s}$$
$$ \approx 2.6 \times 10^{3} \text { years }
$$
