Answer
$$
\alpha=-124 \mathrm{rad} / \mathrm{s}^{2}
$$
or $$|\alpha|=124 \mathrm{rad} / \mathrm{s}^{2}$$
Work Step by Step
(c) The angular acceleration is
$$
\alpha=\frac{d^{2} \theta}{d t^{2}}=-\left(\frac{2 \pi}{T}\right)^{2} \theta_{m} \cos (2 \pi t / T)=-\left(\frac{2 \pi}{T}\right)^{2} \theta
$$
When $\theta=\pi / 4$ ,
$$
\alpha=-\left(\frac{2 \pi}{0.500 \mathrm{s}}\right)^{2}\left(\frac{\pi}{4}\right)=-124 \mathrm{rad} / \mathrm{s}^{2}
$$
or $|\alpha|=124 \mathrm{rad} / \mathrm{s}^{2}$
