Nonlinear vibrations is a field of study concerned with the dynamic behavior of systems described by nonlinear differential equations, where the principles of superposition do not apply and properties like frequency or damping may depend on the amplitude of oscillation. This academic concept investigates complex phenomena such as amplitude-dependent natural frequencies, resonance shifts, bifurcations, multiple stable states, and chaotic dynamics, which are characteristic of many real-world physical and engineering systems where linear approximations are inadequate, making its understanding crucial for accurate modeling, analysis, and design.