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A principle stating that the force needed to extend or compress a spring by some distance is proportional to that distance. Represented by $F = -kx$, where $k$ is the spring constant and $x$ is the displacement. Examples: car suspension, pogo sticks.

The maximum displacement of points in an oscillating system, indicative of the energy in the system. Examples: height of a swing, loudness of a sound (which corresponds to the amplitude of the pressure waves).

The measure of the position of a point in time on a waveform cycle. Examples: the phase difference between voltage and current in AC circuits, the phase relationship between different instruments in a piece of music.

The study of breaking down complex periodic waveforms into a sum of simpler sinusoidal components, referring to the Fourier series or Fourier transform. Examples: signal processing, audio compression.

The graphic representation of a system's oscillations in two perpendicular directions, which can form various shapes depending on the ratio of frequencies and phase differences. Examples: Patterns on an oscilloscope, tuning forks geometry experiments.

The time it takes for one complete cycle of an oscillation. It can be calculated with $T = \frac{1}{f}$, where $f$ is the frequency. Examples: period of a pendulum, time for one swing of a mass-spring system.

A decrease in the amplitude of an oscillation as a result of energy being drained from the system, often due to friction or resistance. Examples: a swinging pendulum coming to rest, a vibrating string stopping.

The measure of opposition that a system presents to the flow of an alternating current (electrical impedance) or sound waves (acoustic impedance). Examples: resistance of speakers to electrical current, the ear's resistance to sound waves.

The frequency at which a system naturally oscillates when not subjected to an external force or damping. Examples: the pitch of a tuning fork, the Earth shaking after an earthquake.

The number of cycles per unit time of an oscillating or repeating event. It is expressed in Hertz (Hz) and given by $f = \frac{1}{T}$, where $T$ is the period. Examples: a vibrating guitar string, AC power supply frequency.

A disturbance that travels through space and matter transferring energy from one place to another. Examples: light waves, sound waves.

The frequency at which the amplitude of a system experiencing two close frequencies fluctuates, given by $f_{beat} = |f_1 - f_2|$, where $f_1$ and $f_2$ are the frequencies being combined. Examples: acoustic beats from two tuning forks, radio frequency interference.

Two or more oscillating systems linked in such a way that energy can be transferred between them. Examples: double pendulum, masses connected by springs.

An integer multiple of the fundamental frequency. It refers to the frequencies that compose the standing wave. Examples: musical notes produced by a guitar string, harmonics in electrical currents.

Oscillation that occurs when a system is subjected to a periodic external force. The frequency of the forced oscillation is determined by the frequency of the external force. Examples: pushing someone on a swing, driving a car over an undulating surface.

A wave that remains in a constant position, typically caused by interference between two travelling waves moving in opposite directions. Examples: vibrating strings on musical instruments, microwave oven cavity.

A higher frequency resonant mode of a system that is a harmonic other than the fundamental mode. Examples: the higher pitched sounds produced from a blown bottle, complex sounds from musical instruments.

A type of periodic motion where the restoring force is directly proportional to the displacement and acts in the direction opposite to that of displacement. Examples: mass on a spring, pendulum for small angles.

A phenomenon in which an external force or a vibrating system drives another system to oscillate with greater amplitude at a specific preferential frequency. Examples: Tacoma Narrows Bridge collapse, swing being pushed.