Answer
$T = 0.44~s$
Work Step by Step
We can use the original period to find the mass of the block:
$T = 2\pi \sqrt{\frac{m}{k}}$
$T^2 = \frac{4\pi^2 m}{k}$
$m = \frac{T^2~k}{4\pi^2}$
$m = \frac{(0.40~s)^2 (600~N/m)}{4\pi^2}$
$m = 2.43~kg$
We can find the new period:
$T = 2\pi \sqrt{\frac{m}{k}}$
$T = 2\pi \sqrt{\frac{2.43~kg+0.50~kg}{600~N/m}}$
$T = 0.44~s$
