A tribute of Ameya Daigavane

Classical Mechanics Level pending

Block $A$ of mass $m$ is performing SHM of amplitude $a$ . Another block $B$ of mass $m$ is gently placed on A when it is at $\frac { a }{ 2 }$ from mean position and $B$ sticks to $A$ . Find amplitude of new SHM.

Details Given $a=1$