A small block mass m is fixed at upper end of a massless vertical spring of spring constant $K=\frac{4mg}{L}$ and natural length 10 L. The lower end of spring is free and is at a height L from fixed horizontal floor as shown. The spring is initially unstretched and the spring block system is released from rest in the shown position.

 

Speed will be maximum when the block passes through the equilibrium position.

$F_{\text{spring }}=mg$
$\therefore$A is correct
(B) From conservation of energy
$mg(\ell +x)=\frac{1}{2}K{x}^2+\frac{1}{2}m{v}_{max}^2$  (1)
Where $x=\frac{mg}{K}=\frac{mg}{4mg}\ell =\frac{\ell }{4}$
Putting $x=\frac{\ell }{4}$ in equation (1)
$V_{max}=\frac{3}{2}\sqrt{gI}$
(C) is incorrect as in equilibrium compression is $\frac{\ell }{4}$ which is more than $\frac{\ell }{8}$
(D) Time taken is $\frac{T}{4}=\frac{1}{4}2\pi \sqrt{\frac{m}{K}}$
$\therefore$D is correct