A horizontal spring block system of mass M executes simple harmonic motion. When the block is passing through its equilibrium position, an object of mass m is put on it and the two move together. Find the new amplitude

Suppose the velocities in the equilibrium position before and after placing the object m and v and v’, and the amplitudes are A and A’ respectively. By conservation of linear momentum we have(M+m)ω'A'=MωA   ⇒M+mA'=MA   ⇒A' =MM+mA