Undergrad Difference between transient and steady state solution

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In driven simple harmonic motion (SHM), the transient response of a system is often ignored once it reaches a steady state, as it is believed to diminish over time. This phenomenon is not exclusive to SHM; all systems with energy storage and dissipation experience a transient phase after being energized. The duration of this transient depends on the system's time constant, and most practical transients are damped, eventually disappearing. Understanding this concept is crucial for comprehending the behavior of oscillatory systems. Resources like HyperPhysics provide additional insights into driven oscillators and their transient responses.
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?
 
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anirocks11 said:
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
 
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cnh1995 said:
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.
 
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