Question

A block of mass m is falling from the height h on to the plate of the spring weight balance (plate’s mass M, spring constant k) as shown. The block sticks to the balance and the system starts to oscillate in the vertical direction. Find the amplitude A of the oscillations

Answer 1

here is the pic

Answer 2

Someone please correct me if I'm wrong!
Using conservation of momentum:
mV1 = (m + M) V2
The initial velocity, right before it hits the plate is found from
PE = KE v1 = (2gh)^(1/2)
Then you can solve for v2, the velocity the plate a block start out with.
This is where I'm not sure:
The initial kinetic energy, with that v2 velocity, is equal to the maximum spring potential (kinetic energy)
1/2(m +M)v2^2 = 1/2 k x^2
Solve for x to get the amplitude.