Answer
$v_{max}=0.224m/s$
Work Step by Step
$v_{max}=\sqrt (\frac{k}{m})A$
where k is the spring constant, m is the mass of the object and A is the amplitude of oscillation.
k=10N/m
m=0.50kg
A=0.050m
So, $v_{max}=\sqrt (\frac{10}{0.50})\times0.050=0.224m/s$