Velocity $v = A \omega \cos \omega t =\frac{\omega A }{2}$

At the time of collision

$\cos \omega t=\frac{1}{2} $

$\omega t=\frac{\pi}{3} \Rightarrow t=\frac{2 \pi}{3}=\frac{\pi}{3} \sqrt{\frac{m}{k}}$

$Image$

for $(C)$ $ \quad time$$ =\frac{2 \pi}{3} \sqrt{\frac{m}{k}}+\frac{\pi}{2} \sqrt{\frac{m}{k}} $

$ =\frac{5 \pi}{6} \sqrt{\frac{m}{k}}$(So it is incorrect) 

for $(D)$ $\quad time  \quad=\frac{2 \pi}{3} \sqrt{\frac{m}{k}}+\pi \sqrt{\frac{m}{k}} $

$ =\frac{5 \pi}{3} \sqrt{\frac{m}{k}} \text { (So it is correct). }$