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  x1=mgK.When block C is attached to B, elongation in spring is  x2=(mgK−a) and speed is zero.Elongation in spring in new mean position is  x3=3mgK.Therefore new amplitude,  a'=x3−x2=(2mgK+a)