$x=x_{0} \cos (\omega t-\pi / 4)$

$\therefore$ Velocity, $v=\frac{d x}{d t}=-x_{0} \omega \sin \left(\omega t-\frac{\pi}{4}\right)$

Acceleration,

$a=\frac{d v}{d t}=-x_{0} \omega^{2} \cos \left(\omega t-\frac{\pi}{4}\right)$

$=x_{0} \omega^{2} \cos \left[\pi+\left(\omega t-\frac{\pi}{4}\right)\right]$

$=x_{0} \omega^{2} \cos \left(\omega t+\frac{3 \pi}{4}\right)$              $...(1)$      

Acceleration, $a=A \cos (\omega t+\delta)$                      $...(2)$

Comparing the two equations, we get

$A=x_{0} \omega^{2}$ and $\delta=\frac{3 \pi}{4}$