Answer
$0.49\frac{m}{s}$
Work Step by Step
In the given scenario
$\frac{1}{2}mv_i^2+\frac{1}{2}Kx_i^2=\frac{1}{2}mv_f^2+\frac{1}{2}Kx_f^2$
This simplifies to:
$v_f=\sqrt{v_i^2+\frac{k}{m}(x_i^2-x_f^2)}$
We plug in the known values to obtain:
$v_f=\sqrt{(0.25)^2+\frac{59}{1.8}[(0.084)^2-(0.042)^2]}=0.49\frac{m}{s}$
