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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?
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).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?
Well pointed out. I wish this generality had been stressed more when I was a student.cnh1995 said:That's not just in SHM. Every system containing energy storing and energy dissipating elements undergoes a transient after it is energized.
A transient solution refers to the behavior of a system over time, where the system is still adapting to changes in its environment. A steady state solution, on the other hand, refers to the behavior of a system when it has reached a stable equilibrium and is no longer changing over time.
This can be determined by analyzing the behavior of the system over time. If the system is still changing and adapting to external stimuli, it is in a transient state. If the system has reached a stable equilibrium and is no longer changing, it is in a steady state.
Yes, both transient and steady state solutions are equally important in scientific research. Transient solutions help us understand how a system adapts to changes, while steady state solutions provide valuable information about the stable behavior of a system.
Transient solutions are typically represented by differential equations, as they involve changes over time. Steady state solutions, on the other hand, can be represented by algebraic equations since there is no change over time.
Yes, a system can have both transient and steady state solutions. For example, a system may initially be in a transient state as it adapts to changes, but eventually reach a steady state once it has reached a stable equilibrium.