Assess students' ability to analyze coupled mass–spring oscillatory systems: derive equations of motion and their matrix form, compute eigenfrequencies and normal modes, decompose arbitrary initial conditions into modal amplitudes, predict time evolution and quantify energy partitioning and transfer between modes, identify and compute beat frequencies, and determine resonance behavior for driven cases. Problems may focus on two-mass examples with extension to N masses and require linear-algebraic modal analysis and ODE solution.