Explanation

(d) Here, $m = 4kg;k = 800Nm^{- 1};E = 4J$
In SHM, total energy is $E = \frac{1}{2}kA^{2}$
where $A$ is the amplitude of oscillation
$\therefore 4 = \frac{1}{2} \times 800 \times A^{2}$
$A^{2} = \frac{8}{800} = \frac{1}{100}$
$\Rightarrow A = \frac{1}{10}m = 0.1m$
Maximum acceleration, $a_{\max} = \omega^{2}A$
$= \frac{k}{m}A\ \ \ \ \ \ \ \ \ \left\lbrack \because\omega = \sqrt{\frac{k}{m}} \right\rbrack$
$= \frac{800Nm^{- 1}}{4kg} \times 0.1m = 20ms^{- 2}$