Examples of sinusoidal in the following topics:

 The solutions to the equations of motion of simple harmonic oscillators are always sinusoidal, i.e., sines and cosines.
 It is called a "sine wave" or "sinusoidal" even if it is a cosine, or a sine or cosine shifted by some arbitrary horizontal amount.
 Uniform circular motion is therefore also sinusoidal, as you can see from .
 The equations discussed for the components of the total energy of simple harmonic oscillators may be combined with the sinusoidal solutions for x(t), v(t), and a(t) to model the changes in kinetic and potential energy in simple harmonic motion.
 Determine factors responsible for the sinusoidal behavior of uniform circular motion

 Phasors are used to analyze electrical systems in sinusoidal steady state and with a uniform angular frequency.
 This can be particularly useful because the frequency factor (which includes the timedependence of the sinusoid) is often common to all the components of a linear combination of sinusoids.
 Sinusoids can be represented mathematically as the sum of two complexvalued functions:
 Sinusoidal Steady State and the Series RLC CircuitPhasors may be used to analyze the behavior of electrical and mechanical systems that have reached a kind of equilibrium called sinusoidal steady state.
 In the sinusoidal steady state, every voltage and current (or force and velocity) in a system is sinusoidal with angular frequency ω.

 For instance, when we studied the forced harmonic oscillator, we first solved the problem by assuming the forcing function was a sinusoid (or complex exponential).
 We then argued that since the equations were linear this was enough to let us build the solution for an arbitrary forcing function if only we could represent this forcing function as a sum of sinusoids.
 Later, when we derived the continuum limit of the coupled spring/mass system we saw that separation of variables led us to a solution, but only if we could somehow represent general initial conditions as a sum of sinusoids.

 But the second term may or may not be a sinusoid, depending on whether the square root is positive.
 First if $\frac{\gamma}{2\omega_0} < 1$ , corresponding to small damping, then the argument of the square root is positive and indeed we have a damped sinusoid.

 If the source varies periodically, particularly sinusoidally, the circuit is known as an alternatingcurrent circuit.
 The voltage and current are sinusoidal and are in phase for a simple resistance circuit.

 The extrema (peaks and troughs) of a sinusoid of frequency $f_s$ will lie exactly $1/2f_s$ apart.

 A general form of a sinusoidal wave is $y(x,t) = A sin(kx\omega t + \phi)$, where A is the amplitude of the wave, $\omega$ is the wave's angular frequency, k is the wavenumber, and $\phi$ is the phase of the sine wave given in radians.
 Since a wave with an arbitrary shape can be represented by a sum of many sinusoidal waves (this is called Fourier analysis), we can generate a great variety of solutions of the wave equation by translating and summing sine waves that we just looked closely into.

 ., sinusoids.The RMS value of a set of values (or a continuoustime function such as a sinusoid) is the square root of the arithmetic mean of the squares of the original values (or the square of the function).
 We can see from the above equations that we can express the average power as a function of the peak voltage and current (in the case of sinusoidally varying current and voltage):
 The RMS values are also useful if the voltage varies by some waveform other than sinusoids, such as with a square, triangular or sawtooth waves .
 The voltage and current are sinusoidal and are in phase for a simple resistance circuit.

 This equation can be solved exactly for any driving force, using the solutions z(t) which satisfy the unforced equation: $\frac{\mathrm{d}^2z}{\mathrm{d}t^2} + 2\zeta\omega_0\frac{\mathrm{d}z}{\mathrm{d}t} + \omega_0^2 z = 0$, and which can be expressed as damped sinusoidal oscillations $z(t) = A \mathrm{e}^{\zeta \omega_0 t} \ \sin \left( \sqrt{1\zeta^2} \ \omega_0 t + \varphi \right)$in the case where ζ ≤ 1.
 In the case of a sinusoidal driving force: $\frac{\mathrm{d}^2x}{\mathrm{d}t^2} + 2\zeta\omega_0\frac{\mathrm{d}x}{\mathrm{d}t} + \omega_0^2 x = \frac{1}{m} F_0 \sin(\omega t)$, where $\!
 \omega$ is the driving frequency for a sinusoidal driving mechanism.

 ., in rotation) or the rate of change of the phase of a sinusoidal waveform (e.g., in oscillations and waves), or as the rate of change of the argument of the sine function.
 Sinusoidal waves of various frequencies; the bottom waves have higher frequencies than those above.