Explanation

(c) When $t = 1\ s,\ y_{1} = r\sin\omega \times 1 = r\sin\omega$
When $t = 2\ s,\ \ y_{2} = r\sin\omega \times 2 = r\sin{2\omega}$
$\therefore\ \ \ \frac{y_{1}}{y_{2}} = \ \frac{r\sin\omega}{r\sin{2\omega}}$
$= \frac{1}{2\cos\omega} = \frac{1}{2\cos{2\pi/T}}$
$= \frac{1}{2\cos{2\pi/8}}$
$= \frac{1}{2\cos{\pi/4}}$
$= \frac{1}{2\left( \frac{1}{\sqrt{2}} \right)} = \frac{1}{\sqrt{2}}$
$\therefore\ \ \ \ \ y_{2} = \sqrt{2}y_{1}$
Distance converted in 2$^{nd}$ second
$= y_{2} - y_{1} = \left( \sqrt{2} - 1 \right)y_{1}$
$\therefore\ \ \ Ratio = 1:(\sqrt{2} - 1)$