Difference between transient and steady state solution

[anirocks11]

In driven SHM, we ignore an entire section of the solution to the differential equation claiming that it disappears once the system reaches a steady state. Can someone elaborate on this?

 

[cnh1995]

In driven SHM, we ignore an entire section of the solution to the differential equation claiming that it disappears once the system reaches a steady state. Can someone elaborate on this?

That's not just in SHM. Every system containing energy storing and energy dissipating elements undergoes a transient after it is energized. Almost all practical transients are damped and they disappear after some time (depending on the 'time constant' of the system).
This might help.
https://www.google.co.in/url?sa=t&s...ghdMAw&usg=AFQjCNGEif9MTJWodsYWTEFg_CkiPt7PTw

 

[S.G. Janssens]

That's not just in SHM. Every system containing energy storing and energy dissipating elements undergoes a transient after it is energized.

Well pointed out. I wish this generality had been stressed more when I was a student.

Here is another clear discussion: HyperPhysics on driven oscillators.