Sinusoidal in the context of "Uniform circular motion"

In telecommunications, a carrier wave, carrier signal, or just carrier, is a periodic waveform (usually sinusoidal) that conveys information through a process called modulation. One or more of the wave's properties, such as amplitude or frequency, are modified by an information bearing signal, called the message signal or modulation signal. The carrier frequency is usually much higher than the message signal frequency because it is usually impractical to transmit signals with low frequencies due to larger wavelength than antenna size.

The purpose of the carrier is usually either to transmit the information through space as an electromagnetic wave (as in radio communication), or to allow several carriers at different frequencies to share a common physical transmission medium by frequency division multiplexing (as in a cable television system).

In psychoacoustics and signal processing, a pure tone is a sound or other signal with a sinusoidal waveform; that is, a sine wave of constant frequency, phase-shift, and amplitude.A pure tone has the property – unique among real-valued wave shapes – that its wave shape is unchanged by linear time-invariant systems; that is, only the phase and amplitude change between such a system's pure-tone input and its output.

Sine and cosine waves can be used as basic building blocks of more complex waves. As additional sine waves having different frequencies are combined, the waveform transforms from a sinusoidal shape into a more complex shape.When considered as part of a whole spectrum, a pure tone may also be called a spectral component.

A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions.

The most general motion of a linear system is a superposition of its normal modes. The modes are "normal" in the sense that they move independently. An excitation of one mode will never cause excitation of a different mode. In mathematical terms, normal modes are orthogonal to each other.

In mechanics and physics, simple harmonic motion (sometimes abbreviated as SHM) is a special type of periodic motion an object experiences by means of a restoring force whose magnitude is directly proportional to the distance of the object from an equilibrium position and acts towards the equilibrium position. It results in an oscillation that is described by a sinusoid which continues indefinitely (if uninhibited by friction or any other dissipation of energy).

Simple harmonic motion can serve as a mathematical model for a variety of motions, but is typified by the oscillation of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's law. The motion is sinusoidal in time and demonstrates a single resonant frequency. Other phenomena can be modeled by simple harmonic motion, including the motion of a simple pendulum, although for it to be an accurate model, the net force on the object at the end of the pendulum must be proportional to the displacement (and even so, it is only a good approximation when the angle of the swing is small; see small-angle approximation). Simple harmonic motion can also be used to model molecular vibration. A mass-spring system is a classic example of simple harmonic motion.