Explanation

(b) The acceleration of a particle in SHM is,
$\alpha_{\max} = - \omega^{2}A$
Where $\omega$ is angular velocity and $A$ the amplitude.
Given, $y = 2\sin\left\lbrack \frac{\pi t}{2} + \varnothing \right\rbrack\ $ …(i)
Standard equation of a wave in SHM is
$y = A\sin{(\omega t + \varnothing)}$ …(iii)
Comparing Eq. (i) with Eq. (ii), we get
$A = 2\ cm,\ \omega = \frac{\pi}{2}$
$\therefore$ $\alpha_{\max} = - \left( \frac{\pi}{2} \right)^{2} \times 2$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \frac{\pi^{2}}{2}\ cms^{- 2}$