The ratio of the maximum velocity and maximum displacement of a particle executing SHM is equal to

$x=Asin(\omega t+\theta )$, thus maximum x occurs at maximum value of sine, i.e. 1, which is x=A
$v=dx/dt=A\omega cos(\omega t+\theta )$, thus maximum v occurs at maximum value of cosine, i.e. 1, which is $v=A\omega$
Thus, ratio is $A\omega /A=\omega$