Final answer:
Using the principles of conservation of momentum and energy, we can solve for the speed of the pan and steak immediately after the collision, the amplitude of the subsequent motion, and the period of that motion in the physics problem involving simple harmonic motion.
Step-by-step explanation:
The student is dealing with a physics problem involving simple harmonic motion (SHM) and conservation of momentum. The mass-spring system, after a totally inelastic collision, exhibits SHM, and we can use physics concepts to solve for the quantities requested in the question.
Speed after Collision
Using conservation of momentum just before and immediately after the collision:
m1v1 + m2v2 = (m1 + m2)vf
Where m1 is the mass of the steak, m2 is the mass of the pan, v1 is the initial velocity of the steak, v2 is the initial velocity of the pan (zero), and vf is the final velocity of both together.
Amplitude
The amplitude is the maximum displacement of the system from its equilibrium position. In this case, it is determined by the energy conservation principle: the potential energy of the steak before it was dropped (m1gh) converts into kinetic energy at the moment of collision, and then, at the equilibrium point after the collision, transforms into the elastic potential energy in the spring (1/2 k x2, where x is the amplitude).
Period of Motion
The period of SHM for a mass-spring system is given by T = 2π√(m/k), where m is the total mass of the system and k is the spring constant. Plugging in the values, we can calculate the period of motion.