Answer
Please see the work below.
Work Step by Step
We know that $v_{max}=\omega A$
and $\omega=\sqrt{\frac{K}{m}}$
Now $K.E_{max}=\frac{1}{2}mv_{max}^2$
$K.E_{max}=\frac{1}{2}m(\frac{KA^2}{m})$
$K.E_{max}=\frac{1}{2}KA^2$
The last equation shows that the maximum kinetic energy does not depend on the mass; that is why both masses have the same maximum kinetic energy.
