Catching a Pellet and Oscillating...?

Question

The following problem is a standard problem found in many physics text books. A block of mass M is at rest on a horizontal frictionless table. It is attached to a rigid support by a spring of constant k. A clay pellet having mass m and velocity v strikes the block from the opposite side that the spring is attached to.

(a) Determine the velocity of the block immediately after the collision.
(b) Determine the amplitude of the resulting simple harmonic motion. In order to solve this problem you must make a number of simplifying assumption; some are stated in the problem and some are not. First, solve the problem as stated.
(c) Discuss the approximations you had to make in order to solve the problem. (There are at least five.)

Explain your work. Thanks! :)

Answer 1

Assumes pellet's velocity, spring alignment and deflection and block's CM are collinear, and that all motion is horizontal. Assumes inelastic collision. Assumes no friction (which is stated). Assumes massless spring and harmonic motion which implies a linear spring. Assumes clay and block are perfectly rigid. And assumes (all together, now) No Air Resistance!
V = mv/(M+m)
Nat. freq. of spring-mass system ω = sqrt(k/(M+m))
Amplitude = V/ω