A mass, M , and spring, k, are at rest in a gravity field, about to be struck by a mass, m, falling from a height, h. The mass, m, sticks to M , and the two move downward. The variable, x, keeps track of the displacement after impact. Sketch the general motion of x for some period of time after impact. How many equations do you think are needed to describe this system mathematically? If the system ever came to rest, what would be the deflection of the spring?
