sinusoidal steady state
(noun) Indicates every voltage and current in a system is sinusoidal with the same angular frequency ω.
Examples of sinusoidal steady state in the following topics:

Phasors
 Describe application of phase vectors in the electrical systems Provide physical definition of a phase vector Phasors are used to analyze electrical systems in sinusoidal steady state and with a uniform angular frequency.
 Phasors may be used to analyze the behavior of electrical systems, such as RLC circuits, that have reached a kind of equilibrium called sinusoidal steady state.
 In the sinusoidal steady state, every voltage and current in a system is sinusoidal with angular frequency .
 In summary, the parameters that determine a cosinusoidal signal have the following units: A, arbitrary (e.g., volts or meters/sec, depending upon the application) ω, in radians/sec (rad/sec) T, in seconds (sec) θ, in radians (rad) τ, in seconds (sec) 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.
 sinusoidal steady state (noun) Indicates every voltage and current in a system is sinusoidal with the same angular frequency .

Driven Oscillations and Resonance
 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.
 The general solution is a sum of a transient solution that depends on initial conditions, and a steady state that is independent of initial conditions and depends only on the driving amplitude
$\!  Steady state variation of amplitude with frequency and damping of a driven simple harmonic oscillator.
 oscillator (noun) A pattern that returns to its original state, in the same orientation and position, after a finite number of generations.
 equilibrium (noun) The state of a body at rest or in uniform motion, the resultant of all forces on which is zero.
 This equation can be solved exactly for any driving force, using the solutions z(t) which satisfy the unforced equation:

Resistors in AC Circuits
 It is the steady state of a constantvoltage circuit.
 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.

Different Types of Currents
 This solution gives the circuit voltages and currents when the circuit is in DC steady state.
 The solution to these equations usually contain a time varying or transient part as well as constant or steady state part.
 It is this steady state part that is the DC solution.

Application of Bernoulli's Equation: Pressure and Speed
 The simplest form of Bernoulli's equation (steady and incompressible flow) states that the sum of mechanical energy, potential energy and kinetic energy, along a streamline is constant.
 The steadystate, incompressible Bernoulli equation, can be derived by integrating Newton's 2nd law along a streamline.
 Bernoulli's equation states that for an incompressible and inviscid fluid, the total mechanical energy of the fluid is constant .

Detonation Waves
 Because the flux of the flow is conserved through the transition, the state of the gas must remain on the chord .
 There is a minimum flux that can pass through the detonation front, , and this flux also corresponds to the minimum velocity jump through the front where the final state is or the Jouguet point.
 Furthermore, for final states above
$O$ along$a'$ the gas leaves the front subsonically.  If the final state lies at
$O$ , the gas leaves the detonation front right at the speed of sound in the downstream flow.  At this point the postshock gas leaves the front at the sound speed so the rarefaction wave no longer overtakes the shock and the combined detonation front and rarefaction wave achieves a steady state.

HalfLife and Rate of Decay; Carbon14 Dating
 Libby estimated that the steadystate radioactivity concentration of exchangeable carbon14 would be about 14 disintegrations per minute (dpm) per gram.

Position, Velocity, and Acceleration as a Function of Time
 One of the most common waveforms in physics is the sinusoid.
 This equation simply states that the acceleration of the waveform (Left: second derivative with respect to time) is proportional to the Laplacian (Right: second spatial derivative) of the same waveform.
 Consider one of the most common waveforms, the sinusoid.
 We looked closely into the sinusoidal wave.
 This graph shows the general form of a sinusoid wave.

RLC Series Circuit: At Large and Small Frequencies; Phasor Diagram
 As for the phase, when a sinusoidal voltage is applied, the current lags the voltage by a 90 phase in a circuit with an inductor, while the current leads the voltage by 90 in a circuit with a capacitor.
 We also learned the phase relationships among the voltages across resistor, capacitor and inductor: when a sinusoidal voltage is applied, the current lags the voltage by a 90º phase in a circuit with an inductor, while the current leads the voltage by 90^{∘} in a circuit with a capacitor.
 Lenz's law (noun) A law of electromagnetic induction that states that an electromotive force, induced in a conductor, is always in such a direction that the current produced would oppose the change that caused it; this law is a form of the law of conservation of energy.

Maxwell's Equations
 The field (E) points towards negative charges and away from positive charges, and from the microscopic perspective, is related to charge density (ρ) and permittivity (ε_{0}) as:
$\nabla \cdot \bf E=\frac {\rho}{\epsilon_0}$ Gauss's law for magnetism states that there are no "magnetic charges" analogous to electric charges, and that magnetic fields are instead generated by magnetic dipoles.  Both macroscopic and microscopic differential equations are the same, relating electric field (E) to the timepartial derivative of magnetic field (B):
$\nabla \times \bf E=\frac {\partial \bf B}{\partial t}$ Ampere's law originally stated that magnetic field could be created by electrical current.  Electric (red) and magnetic (blue) waves propagate in phase sinusoidally, and perpendicularly to one another.
 The field (E) points towards negative charges and away from positive charges, and from the microscopic perspective, is related to charge density (ρ) and permittivity (ε_{0}) as: