sinüzoidal

Sinüzoidal is an adjective used in Turkish to describe something that has the shape or character of a sine wave. In mathematics and engineering, a sinüzoidal waveform is the same as a sinusoidal waveform, referring to a signal that follows a sine or cosine function of time. The term is commonly used in Turkish texts as well as in bilingual contexts where the English term sinusoidal is relevant.

Mathematically, a pure sinüzoidal signal can be written as y(t) = A sin(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase. The frequency is f = ω/(2π) and the period is T = 2π/ω. Such signals have constant amplitude and frequency in ideal conditions and are periodic and smooth. In the complex form, they can be expressed as the real part of A e^{i(ωt+φ)}.

Sinüzoidal waves are foundational in many areas because they are solutions to linear differential equations with constant coefficients, such as the simple harmonic oscillator. They also underpin Fourier analysis: any periodic signal can be decomposed into a sum of sinüzoidal components with different frequencies, and a single sinüzoidal signal contains exactly one frequency component.

Applications of sinüzoidal signals include alternating current power, radio and audio communications, vibration analysis, and control systems. In practice, real-world signals are often not purely sinüzoidal but can be approximated by a combination of sinusoidal components. The term sinüzoidal thus both describes an idealized sine-shaped waveform and, by extension, approximations used in engineering and physics.