In a simple harmonic motion,

Maximum acceleration, $f_{max}={\omega }^{2}A$

Maximum velocity, $v_{\max }=A\omega$. 

$\frac{f_{\max }}{v_{\max }}=\frac{{\omega }^{2}A}{A\omega }=\omega$

$\omega =10$

Displacement in SHM is $x=A\sin \left(\mathrm{\omega t}+\frac{\pi }{4}\right)$

At $t=0$

$5=A\sin \left(\frac{\pi }{4}\right)$

$A=5\sqrt{2}$. 

Max acceleration = ${\omega }^{2}A$

$=100\times 5\sqrt{2}$

$=500\sqrt{\mathrm{2 }} \mathrm{m} {\mathrm{s}}^{-2}$