Answer
(a) t = 0.150 s
(b) t = 0.075 s
Work Step by Step
(a) We can find the angular frequency.
$\omega = \frac{2\pi}{T}$
$\omega = \frac{2\pi}{0.900~s}$
$\omega = 6.98~rad/s$
We can write the general equation for the position.
$x = A~cos(\omega~t)$
We can find $t$ when $x = \frac{A}{2}$.
$x = A~cos(\omega~t)$
$\frac{A}{2} = A~cos(\omega~t)$
$cos(\omega~t) = \frac{1}{2}$
$t = \frac{arccos(\frac{1}{2})}{\omega}$
$t = \frac{\frac{\pi}{3}}{6.98~rad/s}$
$t = 0.150~s$
(b) We can find $t$ when $x = 0$.
$x = A~cos(\omega~t)$
$0 = A~cos(\omega~t)$
$cos(\omega~t) = 0$
$t = \frac{arccos(0)}{\omega}$
$t = \frac{\frac{\pi}{2}}{6.98~rad/s}$
$t = 0.225~s$
The time to move from $x = \frac{A}{2}$ to $x = 0$ is $0.225~s-0.150~s$, which is $0.075~s$.
