Physics of transients -- general

[houlahound]

Recalling my reading on a variety of physical systems solutions were always defined for some time after the system is energised.

For example circuits, waves...

For these systems a whole lot of complex, "stuff" eg sloshing around of energy, occurs to result in a stable value in time, stable does not imply constant here.

For discussion how would one analyse

1. the signals in an AC simple circuit as soon as it is energised up to the time you get a stable output that is the same as what you would measure.

2. The amplitudes of a string as it goes from one overtone to the next.

Is such analysis even possible to write??

Is the knowledge of transient states useful or revealing of anything??

I get experimenters only are interested in what they measure is the measurable steady state values.

Just a curiosity question,

 

[cnh1995]

the signals in an AC simple circuit as soon as it is energised up to the time you get a stable output that is the same as what you would measure.

You can write the differential equation and solve it using initial conditions. The solution will contain two parts: complementary solution (transient)+ particular integral (steady state). The transient decays exponentially depending on the time constant of the circuit.
In ac circuits, this transient depends on the instant of switching (energizing). If the switching instant is at steady-state current zero crossing, there is no transient. If the switching instant is +- 90° w.r.t. the current zero crossing, the transient is maximum.

 

[houlahound]

So a circuit just decays from an exponential to a sine?

What if a multi-frequency source is used?

 

[cnh1995]

So a circuit just decays

From dc+sine to just sine, decaying exponentially.

What if a multi-frequency source is used?

You mean two sources with different frequency?

 

[houlahound]

Well no limit on the number of frequencies.

Just want to know what math handles it, DE's in time domain evidently.

ETA, is this (transients) useful (or interesting) for say designers or phycisists?

 

[cnh1995]

is this (transients) useful (or interesting) for say designers or phycisists?

Very much. In electrical power system, this analysis is very important in designing the circuit breakers since they operate in a few cycles after the occurrence of fault. The symmetrical and unsymmetrical breaking capacities of the CBs are calculated from the transient analysis.

For multiple frequencies, superposition theorem is used. Time response for each frequency is calculated separately and then they are added as per the superposition theorem.

 

[houlahound]

Sounds interesting, any links to resources to get my reading started.

Thanks for responses, I want to follow this stuff up.

 

[cnh1995]

Sounds interesting, any links to resources to get my reading started.

Thanks for responses, I want to follow this stuff up.

Google "ac transient analysis".

https://www.google.co.in/url?sa=t&s...ggrMAM&usg=AFQjCNF7YZ49WachTfM4bTUvsDiqBEf3tw

 

[houlahound]

That NPTEL site going to keep me busy for awhile, thanks for link.

 

[sophiecentaur]

2. The amplitudes of a string as it goes from one overtone to the next.

In a linear system, i think it has to be true to say that the behaviour of the normal modes is independent. The modes will all have different damping coefficients.

 

[Nidum]

(1) For many real systems the transient response of the system can be as or more important than the steady state response to a control function .

The jet engine is one good example . An engine capable of working normally over a range of different steady state conditions can become unstable during transition from one steady state to another . In modern times this instability is designed out as far as possible but there have been many engines in the past where the control inputs just had to be scheduled in such a way that instability could not occur .

(2) A different example is a modern robot or CNC machine tool .

These types of machines seldom or maybe never work in a steady state condition . Continually changing control inputs generate continually changing responses . The machines are in a continual state of transition . So this requires an understanding of transient responses at a much deeper level than for the very simple one variable one event problems which most students are shown .

Designing control systems for these machines is a complex and fascinating subject involving many different areas of engineering .

 

[cnh1995]

That NPTEL site going to keep me busy for awhile, thanks for link.

@houlahound, if you are still pursuing this topic, you might want to see these simulation results from an ongoing thread in the EE forum.
https://www.physicsforums.com/posts/5797346/