What exactly is steady-state solution? In solving differential equation, one encounters steady-state solutions. My textbook says that steady-state solution is the limit of solutions of (ordinary) differential equations when $t \rightarrow \infty$. 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?

Example from dynamics: You can picture for yourself a cantilever beam which is loaded by a force at its tip say: $F(t) = \sin(t)$. 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. You can expand this thinking to other differential equations as well. Hope that helps.
