In the figure the two blocks A and B, each of mass m, are oscillating with amplitude a. When block B is at its highest position, another block C of mass 2m is gently placed on it. New amplitude of oscillation will become (pulley is smooth)

When A and B are oscillating, elongation in mean position is  $x_1=\frac{mg}{K}.$
When block C is attached to B, elongation in spring is  $x_2=(\frac{mg}{K}-a)$ and speed is zero.
Elongation in spring in new mean position is  $x_3=\frac{3mg}{K}.$
Therefore new amplitude,  $a^{\text{'}}=x_3-x_2=(\frac{2mg}{K}+a)$