Let the velocity of M before sticking M be v0, then the system energy E0 = MV0 2/2 = Ka0 2/2...( 1).

The velocity v of the attached system is conserved by momentum: (m+M)v=mv0.

Therefore, v=mv0/(M+m) At this time, the energy of the system e = (m+m) v2/2 = (mv0) 2/2 (m+m) = ka 2/2 ... (2).

From (1)(2):

A0:A=√(M+m):√m