Explanation

(a) $x = 5\sqrt{2}(\sin{2\pi t + \cos{2\pi t}})$
$= 5\sqrt{2}\sin{2\pi t + 5\sqrt{2}\cos{2\pi t}}$
$x = 5\sqrt{2}\sin{2\pi t + 5\sqrt{2}}\sin\left( 2\pi t + \frac{\pi}{2} \right)$
Phase difference between constituent waves $\phi = \frac{\pi}{2}$
$\therefore$ Resultant amplitude $A = \sqrt{\left( 5\sqrt{2} \right)^{2} + \left( 5\sqrt{2} \right)^{2}} = 10\ cm$