# Homework Help: Overdamped system

1. Jan 12, 2016

### Ivan Antunovic

1. The problem statement, all variables and given/known data
When we have a damped system,we have 3 types of responses of the system,what really determines how our system will behave?

2. Relevant equations
$$\alpha = R/2L$$
$$\Omega = 1/LC$$

3. The attempt at a solution
Overdamped system solution is $$x(t)=A1*exp(\alpha+\sqrt(\alpha^2-\omega^2) + A2* exp-(\alpha+\sqrt(\alpha^2-\omega^2)$$,this green exponential decay is when one of the constants is zero I guess,because then we have exp(-t),what about other curves?

Last edited by a moderator: Jan 12, 2016
2. Jan 12, 2016

### donpacino

I suggest you look at the system in the frequency domain.

3. Jan 12, 2016

### Staff: Mentor

Your solution should be a function of t, which doesn't appear on the right side above.
The system is modelled by a 2nd order differential equation. The roots of the characteristic equation for the differential equation determine whether the system is overdamped, underdamped, or critically damped.

4. Jan 13, 2016

### Ivan Antunovic

Yes,I know that roots determine system behaviour,what I wonder is about DAMPED system,we have 3 variations of the response and I forgout to multiply by t

5. Jan 23, 2016

### Ivan Antunovic

I am really sad that none actually understood my question,what I figured out,those 3 graphs are determined by initial conditions, for the blue one if the capacitor has initial voltage as on the picture it will produce a current that has the same direction as the initial current of the inductor,that's why we have a little 'spike' over value of 1.(they are being added up)

The red graph ,is when we have initial voltage on the capacitor producing a current in ic in the opposite direction of the initial current in the inductor ,and therefore we have a negative 'spike' ,because in the scenario of the blue graph currents add up,and here one current will have bigger value than the other one.

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6. Jan 24, 2016

### Staff: Mentor

The middle graph is what would result when the capacitor has an initial voltage but there is no initial current in the inductor.

I think you might have the direction of initial IL around the wrong way for red and blue, but anyway your idea sounds spot on.

I'm not sure that the values of RC and L that give rise to the red curve would, without change, also be able to produce the blue and green curves, but a simulation would easily confirm this is so just by setting different values for IL(0).

7. Jan 24, 2016

### Ivan Antunovic

Do you have a suggestion for some good simulation program?Maybe proteus demo?

8. Jan 24, 2016

### donpacino

9. Jan 24, 2016

### donpacino

write the equations for the circuit out. In your initial post you gave us no indication of what this system was...........

10. Jan 24, 2016

### Ivan Antunovic

I wrote that it's a overdamped system ,and gave you the equation of the system,I really don't see how equations gonna help you out with this one?

11. Jan 24, 2016

### donpacino

If you either
or
B. don't give us the information we need to give you advice

don't be upset when you are not happy with the results.

Looking at the governing equations (preferably in the frequency domain) will tell you how the component values and the initial conditions will effect the transient conditions.

where did you get the equation from post #1?
is there any other information you are withholding from us?

12. Jan 24, 2016

### donpacino

what is your backround in electronics?

IL(0-) cannot be anything but 0 (assuming the switch closes at t=0)

if it opens at t=0 that is a different story

13. Jan 25, 2016

### amsi

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14. Jan 25, 2016

### Ivan Antunovic

Well man,I've made a mistake,I forgot to add a voltage/current source in the parallel,my background is very good at electronics,but this doesn't have to do anything with electronics,it's circuit theory.

This equation is from lecture notes , MIT.

Okay this picture is from a book 'Linear and non linear electrical circuits',it shows the equation
http://postimage.org/] [/PLAIN] [Broken]
image hosting sites

And writing down the equation will give me only general solution to the equation,it doesn't say what determines those 3 graphs,it's obvious that initial conditions determine those 3 graphs.And I wasn't upset,I just had a feeling that none understood me.

Last edited by a moderator: May 7, 2017
15. Jan 25, 2016

### donpacino

ok. if you think there is a large difference between electronics and circuit theory, then what is your background in circuit theory.

developing a mathematical model of the system is very important. from the mathematical model you can see what parameters will effect the outputs in which way. If you have a mathematical model in the frequency domain, you can clearly see the poles and zeros. from there evaluating the poles and zeros will show which parameters will effect the output.

what is the actual question you are trying to answer? all of it.
Are you given a circuit? or are you only given graphs?

If you are given graphs, you can make no assumptions about the circuit, and you need to answer the question mathmatically. where the switch is, and where the sources are will effect the output drastically, if there is even a circuit.

Last edited by a moderator: May 7, 2017
16. Jan 25, 2016

### donpacino

look up dominant zeros.
it may help you, if you either derive a mathematical expression for the circuit, or don't have a circuit and only need a mathematical answer.

17. Jan 25, 2016

### Ivan Antunovic

The professor asked me 'what determines those 3 graphs' that was the question.

18. Jan 25, 2016

### donpacino

ok... if that was the entire question, and there is no included or implied circuit, then i would recommend looking up dominant zeros. Or the answer is simply the initial condition

19. Jan 26, 2016

### Ivan Antunovic

Sorry I am not native english speaker, what do you mean looking up dominant zeros?

20. Jan 26, 2016

### donpacino

have you done any work with transfer functions in the frequency domain?
do you know what poles or zeros are?

if you have not worked with the frequency domain this explanation will not be sufficient.

a dominant zero is when a system has a zero that is smaller or close to the smallest pole of the system.

look at the above link. page 4 will kind of explain what poles and zeros are.
you can see on page 43-46 the effects of the zeros. you should then be able to explain the effects of the graphs you showed above.

21. Jan 26, 2016

### Staff: Mentor

Take a closer look. The 3 step responses pictured in this graph are clearly not illustrating a variation in poles and zeros or damping.

Last edited: Jan 26, 2016
22. Jan 26, 2016

### donpacino

i respectfully disagree. the red and blue lines are produced by dominant zeros.

edit: the red and blue lines CAN BE produced by dominant zeros.

23. Jan 26, 2016

### Staff: Mentor

There a more than 2 plots. They all show a system that starts at a common level, and falls back to a lower level.

The peak in the blue plot can be explained only by a change in initial conditions.

24. Jan 26, 2016

### donpacino

a systems poles and zeros do not effect the start level or end level

25. Jan 26, 2016

### Staff: Mentor

Poles and zeros do not cause a ZSR to initially veer off in the wrong direction, which is what the blue curve does.