vibration

Vibration is the rapid oscillation of an object around an equilibrium position. It can be true free vibration, where no external force sustains the motion, or forced vibration, where an external periodic force drives the motion. Vibration occurs in solids, liquids, and gases and is a common phenomenon in engineering, physics, and daily life.

In simple terms, a vibrating system is characterized by displacement, velocity, and acceleration as functions of time. The amplitude measures the size of the motion, the frequency or cycles per second (hertz) the rate, and the period is the reciprocal of frequency. For many systems the motion can be approximated as simple harmonic motion, in which displacement x(t) = A cos(ωt + φ) with ω = 2πf.

Most real systems include damping, described by a term proportional to velocity that removes energy. The standard linear model is m x'' + c x' + k x = F(t). Depending on parameters, the response can be underdamped, critically damped, or overdamped, affecting how quickly vibrations die out.

Resonance occurs when the forcing frequency matches the natural frequency of the system, producing large amplitudes. Engineers must consider resonance to avoid fatigue and failure, or to design devices such as resonators and filters.

Vibration is measured with accelerometers, velocity sensors, or displacement probes. Analysis often uses time-domain signals and frequency-domain tools such as Fourier transforms to identify dominant frequencies and magnitudes.

Applications include machinery condition monitoring, building and bridge design to withstand earthquakes, automotive and aerospace components, and consumer electronics. Unwanted vibration can cause noise, wear, and health issues, so vibration isolation, damping, and control are important design considerations.