vibrations

Vibrations are oscillations about an equilibrium position that repeat in time. They occur in mechanical structures, fluids, gases, electrical systems and even at molecular scales. Vibrations can be free, occurring when a system is displaced and then allowed to move without further forcing, or forced, when an external source continuously drives the motion. They may be periodic, as in a tuning fork, or random, as in turbulent flow.

Key parameters include amplitude, frequency, and period. The phase describes the position within a cycle. The natural frequency is the frequency at which a system tends to vibrate when disturbed; damping reduces amplitude over time. If the driving frequency matches the natural frequency, resonance can occur, producing large amplitudes and potential damage or noise.

Many vibrating systems are modeled by differential equations. A simple mass–spring–damper follows m x'' + c x' + k x = F(t). Without forcing, x'' + (c/m) x' + (k/m) x = 0. Depending on damping, responses are underdamped, critically damped, or overdamped. In continuous systems, vibration modes or normal frequencies arise from spatial structure.

Vibrations are studied across disciplines and have practical applications. They are central to engineering design, safety, and reliability, and appear in structural dynamics, acoustics, machinery vibration analysis, and musical instruments. In solids, vibrational energy is carried by phonons.

Measurement and control rely on accelerometers, laser vibrometry, and spectral analysis such as Fourier transforms. Mitigation strategies include isolation, damping, updated materials, or design changes to avoid resonance and reduce fatigue, noise, and wear.