Final answer:
To describe a two-mass system with differential equations, identify the system of interest, draw a free-body diagram, and apply Newton's second law of motion, considering both linear and possible rotational motion.
Step-by-step explanation:
To find the set of differential equations describing a two-mass system, one must first determine the system of interest. After establishing the system to analyze, it's crucial to draw a free-body diagram, which involves detailing all the external forces acting on the system. Then, Newton's second law of motion is used in conjunction with the free-body diagram to describe the motions of the system. Newton's second law of motion can be written as F = ma, where F represents the net force applied to the system, m is the mass of the system, and a is the acceleration.
For the given system in the question, one has to apply Newton's second law separately for each mass, considering the forces acting on each and the constraints between them. If the system involves rotational motion, then the rotational equivalent of Newton's second law, ΣT = Iα, should be used, where ΣT is the net torque, I is the moment of inertia, and α is the angular acceleration.
To ensure that the solution is reasonable, check the results against the physical constraints and initial conditions of the system.