Explanation

(b) If at any instant displacement is $y$ then it is given that
$U = \frac{1}{2} \times E \Rightarrow \frac{1}{2}m\omega^{2}y^{2} = \frac{1}{2} \times \left( \frac{1}{2}m\omega^{2}a^{2} \right)$
$\Rightarrow y = \frac{a}{\sqrt{2}} = \frac{6}{\sqrt{2}} = 4.2\ cm$