What is Steady state: Definition and 175 Discussions

In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so:








p



t



=
0


for all present and future

t
.


{\displaystyle {\frac {\partial p}{\partial t}}=0\quad {\text{for all present and future }}t.}
In discrete time, it means that the first difference of each property is zero and remains so:





p

t




p

t

1


=
0


for all present and future

t
.


{\displaystyle p_{t}-p_{t-1}=0\quad {\text{for all present and future }}t.}
The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering. If a system is in a steady state, then the recently observed behavior of the system will continue into the future. In stochastic systems, the probabilities that various states will be repeated will remain constant. See for example Linear difference equation#Conversion to homogeneous form for the derivation of the steady state.
In many systems, a steady state is not achieved until some time after the system is started or initiated. This initial situation is often identified as a transient state, start-up or warm-up period. For example, while the flow of fluid through a tube or electricity through a network could be in a steady state because there is a constant flow of fluid or electricity, a tank or capacitor being drained or filled with fluid is a system in transient state, because its volume of fluid changes with time.
Often, a steady state is approached asymptotically. An unstable system is one that diverges from the steady state. See for example Linear difference equation#Stability.
In chemistry, a steady state is a more general situation than dynamic equilibrium. While a dynamic equilibrium occurs when two or more reversible processes occur at the same rate, and such a system can be said to be in a steady state, a system that is in a steady state may not necessarily be in a state of dynamic equilibrium, because some of the processes involved are not reversible.

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  1. Wrichik Basu

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    ##\require{physics}##The given circuit is this: The question is taken from this video. The Professor has solved it using Phasor analysis, the final solution being $$\begin{equation} i_x(t) = 7.59 \sin \qty( 4t + 108.4^\circ )~\mathrm{amps}. \end{equation}$$My aim, however, is to use Laplace...
  2. huangdaiyu

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  3. L

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  4. fluidistic

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  5. R

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  6. TheHeraclitus

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  7. S

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  8. nobodyjusttrying

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  9. M

    MHB What is the maximum yield for a steady state solution?

    I've got a question here which I'm really unsure what the wording is asking me to do, I've calculated (5), so worked out the steady states. However question 6 has really thrown me off with it's wording, any help would be appreciated.
  10. M

    MHB Steady State Question Understanding

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  11. M

    MHB Find Steady States for Equations: u, v and Get Help with Steady State Question

    Got a steady state question and was wondering if anyone would be able to check if I'm on the right track? Find the steady states of these two equations: My working out as far: \[ 0=u*(1-u*)(a+u*)-u*v* \] \[ 0=v*(bu*-c) \] I looked at the 2nd equation first giving: \[ v*=0, u*=c/b \]...
  12. Richard Parker

    I Difference between stationary and steady state

    I was recently working on a problem of Griffiths and in the solution's manual it used an argument to solve a diffential equation that caught my attention. It said that it would look first to the steady state solution of the ODE. I tought "All right, I get that" but when I got to translate the...
  13. dvscrobe

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  14. J

    Could someone help with this steady state capacitors questio

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  15. D

    Air Compressor Model Analysis

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  16. Krushnaraj Pandya

    Energy in capacitor at steady state

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  17. M

    What does steady state mean for a pendulum?

    Hi there. I am working on some exercises where they ask about the steady state of a pendulum. I have had quantum mechanics, where the steady state meant a time independence. But I don't really see what this means for a pendulum. Is it steady when it's velocity is zero so there is no time...
  18. S

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  19. Dor

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  20. S

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  21. S

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  22. Z

    Magnitude of the transfer function

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  23. T

    Heat gain (or Loss) in steady state from Metal Rod

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  24. A

    I Difference between transient and steady state solution

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  25. C

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  26. AGiantGolden49er

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  27. H

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  28. N

    MATLAB I with matlab designing a steady state feedback H2 control system

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  29. A

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  30. Hannibal247

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    Hello, Im having some issues with my task. 1. Homework Statement The heat generation rate of a cylindrical fuel (D=0.2 m and 1 m long) is 160 kW. The thermal conductivity of the fuel is 100 W/mK and its surface temperature is maintained at 283 K. Determine the temperature at the axis...
  31. T

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    Homework Statement A damped harmonic oscillator is driven by an external force of the form $$F_{ext}=F_0sin(\omega t)$$ Show that the steady state solution is given by $$x(t)=A(\omega)sin(\omega t-\phi)$$ where $$ A(\omega)=\frac{F_0/m}{[(\omega_0^2-\omega^2)^2+4\gamma^2\omega^2]^{1/2}} $$ and...
  32. K

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  33. B

    Solving a System of ODE for Steady State

    I am trying to find the steady states in the ODE system. Assuming y0 = 2.5 * 10^5, I want to calculate y1, y2, y3 at the steady state. I do not understand how this would be possible, because only y0 is given and the following: d0 = 0.003, d1 = 0.008, d2 = 0.05, d3 = 1, ry = 0.008, ay = 1.6/100...
  34. S

    What is the voltage in the inductor or capacitor for a short/open circuit?

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  35. T

    Steady State Distillation Process

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  36. j3dwards

    Circuit settles to steady state and switch is opened

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  37. RJLiberator

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  38. kartmaze

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  39. O

    Steady state temp. distribution

    Homework Statement Homework Equations ıt is nonhomog type ,2D heat conduction problem The Attempt at a Solution I don't understant To parts so I couldn't attemp a solution.
  40. K

    Steady state excess carrier - Semiconductor

    Please check the following questions. Steady state of semiconductor w.r.t excess carrier. 1. If we shine photons on semiconductor and then turn the light off, semiconductor is not under the steady state condition. (it is under transient state since excess carrier concentration is decreasing)...
  41. jdawg

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    Homework Statement DC steady state circuit analysis: Consider the circuit shown below. The switch shown in the problem opens at time t = 0 seconds. If the circuit is in DC steady state at , find values for iL(0-), iL(0+), i(0-), i+, Vc(0-), Vc(0+). There is no RL or RC analysis to be performed...
  42. J

    Steady State Heat Equation with Source

    I am trying to solve the steady state heat equation with a heat source. I am starting out in 1 dimension (my book gives the solution in 2, but I'm just trying to get a feel right now) and I have a heat source Q, located at 0. It radiates heat through an infinite medium. So what would the steady...
  43. leafjerky

    Thermodynamics - Steady State Nozzle, find area of inlet/exit

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  44. T

    How do you work out wave envelopes and asymmetries?

    Hi Say I took one or all of the four waves here: How would I go about working out the envelope around their peaks, or finding the exponential time constant from start to steady state? Cheers!
  45. D

    Driven damped oscillator

    Homework Statement A small block (mass 0.25 kg) attached to a spring (force constant 16 N/m) moves in one dimension on a horizontal surface. The oscillator is subject to both viscous damping and a sinusoidal drive. By varying the period of the driving force (while keeping the drive amplitude...
  46. F

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  47. M

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  48. B

    Two differential equations -- Need to find steady state values

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  49. J

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