What exactly is steady-state solution? In solving differential equation, one encounters with steady-state solution. My textbook says that steady-state solution is the limit of solutions of (ordinary) differential equations when PSKt \Rightarrow \inftyZSK. But the steady-state solution is given as f(t), and this means that the solution is a function of t - so what is this t being in limit?

Karli Kidd

Karli Kidd

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2022-08-17

What exactly is steady-state solution?
In solving differential equation, one encounters with steady-state solution. My textbook says that steady-state solution is the limit of solutions of (ordinary) differential equations when t. But the steady-state solution is given as f(t), and this means that the solution is a function of t - so what is this t being in limit?

Answer & Explanation

Jovany Mathews

Jovany Mathews

Beginner2022-08-18Added 8 answers

Steady state means some properties of the system are unchanging wrt to time. It usually occurs after some time the process is initiated. Corresponding solutions are the steady state solutions.
Nashorn0o

Nashorn0o

Beginner2022-08-19Added 3 answers

Example from dynamics: Visualize a cantilever beam that is loaded at its tip by the following force: F(t)=sin(t). At t=0 the force is applied, then you get the transient state, after some time the system will become in equilibrium: the steady-state. In this state no changes are applied to the system. This concept can also be applied to other differential equations. Hope that was useful.

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