horizontal block-spring system

Yes, you should use conservation of momentum because there is no external force acting on the system.

a. By the law of conservation of momentum

Initial momentum = Final momentum

mv = (M + m)v'

Velocity of the block immediately after impact, v' = mv / (M + m)

b. Now, we can use the law of conservation of energy

K.E. of the system immediately after impact = E.P.E. of the system when it is instantaneously at rest

1/2 (M + m)v'^2 = 1/2 kA^2

m^2v^2 / (M + m) = kA^2

Amplitude, A = mv sqrt[1 / k(M + m)]