c
(c)
If there was no collision each spring will oscillate with period
$T=2 \pi \sqrt{\frac{m}{k}}$
Because of collisions the springs are only compressed but cannot extend beyond their natural length. Hence the perform only half oscillation.
Hence $\quad T=2 \pi \sqrt{\frac{m}{k}} \div 2$
or $T=\pi \sqrt{\frac{m}{k}}$