sinusoidal steady state
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
 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.

Driven Oscillations and Resonance
 , and which can be expressed as damped sinusoidal oscillations in the case where ζ ≤ 1.
 , where is the driving amplitude and is the driving frequency for a sinusoidal driving mechanism.
 Steady state variation of amplitude with frequency and damping of a driven simple harmonic oscillator.

Resistors in AC Circuits
 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.

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.
 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
 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.
 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.

Time
 The second is now operationally defined as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom."
 It follows that the hyperfine splitting in the ground state of the cesium 133 atom is exactly 9,192,631,770 hertz .
 In other words, cesium atoms can be made to vibrate in a very steady way, and these vibrations can be readily observed and counted.

Maxwell's Equations
 Gauss's law for magnetism states that there are no "magnetic charges (or monopoles)" analogous to electric charges, and that magnetic fields are instead generated by magnetic dipoles.
 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.

Electric Charge in the Atom
 In the ground state, an atom will have an equal number of protons and electrons, and thus will have a net charge of 0.