and $v = \frac{{dx}}{{dt}} = - a\omega \sin (\omega \,t + \theta )$ ….(ii) 

Given at $t = 0$, $x = 1\,cm$ and $v = \pi $ and $\omega = \pi $ 

Putting these values in equation (i) and (ii) we will get $\sin \theta = \frac{{ - 1}}{a}$ and $\cos \theta = \frac{1}{A}$ 

==> ${\sin ^2}\theta + {\cos ^2}\theta = {\left( { - \frac{1}{a}} \right)^2} + {\left( {\frac{1}{a}} \right)^2}$

==> $a = \sqrt 2 \,cm$