A snowball of mass 100g is thrown with a velocity of 10 m/s horizontally on a box on a frictionless table. The box is connected to a spring which is attached to the wall. The box is of mass 1.0kg. The entire snowball is attached to the box and it is observed that the box is compressed 16 cm at most after the snowball hits the box.
a) explain why this starts the system to be in simple harmonic motion.
b) find the period for the oscillation of the system.
c) what happens too the period if the snowball falls off and the box is the only thing oscillating.
I think I got the first problem right, it is in simple harmonic motion because the force of the snowball is the only force acting on the system, so the acceleration is directly proportional to the displacement. a= -kx/m (by hooks law, newtons 2. and 3. law)
In the second problem I have calculated the final velocity by use of the conservation of momentum in perfectly inelastic collisions. But I can't figure out how to proceed from here. Since I think I have to find the spring constant, but I dont know how to find it.
All help is appreciated!