help please?

Question

2. A block of mass M, at rest on a horizontal
frictionless table, is attached to a rigid support
by a spring of constant k. A bullet of mass m
and velocity v strikes the block. The bullet remains embedded in the block.

1) (a) Determine the velocity of the block immediately after the collision (in terms of M,m and v).
Hints: What kind of collision is it? Is mechanical energy conserved? Is momentum conserved?

2) (b) Determine amplitude of the resulting simple harmonic motion (in terms of M, m,v and k).
Hints: In which form is the energy right after the collision? Is mechanical energy
conserved in simple harmonic oscillations? How amplitude is related to
the energy?

http://physics.syr.edu/courses/PHY211.07Spring/hw/HWProblemSet12.pdf

Answer 1

Since this is an inelastic collision, momentum is conserved. This instantaneous velocity can be calculated as
m*v=(M+m)*v2
v2=m*v/(M+m)

The mechanical energy is conserved in this case. To comput e the energy of the system, start with
.5*(M+m)*(m*v/(M+m))^2
=0.5*k*A^2
(This is the compression of the spring after collision)
simplify
A=m*v/sqrt((M+m)*k))

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