Answer
$D\lt C\lt A\lt B$
Work Step by Step
We know that the time period is given as
$T=2\pi \sqrt{\frac{m}{K}}$
For system A
$T_A=2\pi \sqrt{\frac{m_A}{K_A}}=2\pi\sqrt{\frac{m}{K}}$
For system B
$T_B=2\pi\sqrt{\frac{2m}{K}}=\sqrt{2}T_A$
For system C
$T_C=2\pi \sqrt{\frac{3m}{6K}}=\frac{1}{\sqrt 2}T_A$
For system D
$T_D=2\pi \sqrt{\frac{m}{4K}}=\frac{1}{2}T_A$
Now the increasing order of the time periods of the given systems is
$D\lt C\lt A\lt B$
