The ratio of maximum acceleration to maximum velocity in a simple...

In a simple harmonic motion,

Maximum acceleration, {f}_\max = {\omega}^{2}A

Maximum velocity, {v}_\max = A\omega.

\dfrac{{f}_\max}{{v}_\max} = \dfrac{{\omega}^{2}A}{A\omega} = \omega

$\omega = 10$

Displacement in SHM is $x = Asin \left(\omega t + \dfrac{\pi}{4}\right)$

At $t = 0$

$5 = Asin \left(\dfrac{\pi}{4}\right)$

$A = 5\sqrt{2}$.

Max acceleration = ${\omega}^{2}A$

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

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