# Sketch waveform to represent the transient response

No, and I can see that clearly on many graphs on the subject.

donpacino
Gold Member
No, and I can see that clearly on many graphs on the subject.
so an overdamped system will slowely rise to the end value, kind of like a first order response. You'll see that it will never actually reach 100%, and will not have any overshoot

Yes, I also understand that too. I guess the formulas I'm using are only valid for values up to zeta=1. I think that, what I'm currently studying only scratches the surface of this subject.
Why I've questioned this and because they don't just give you a value of Zeta, but also include a value of an I damped natural frequency wo. Why give both values to sketch a graph after all?

Are there any relationships between different values of Zeta, as you can clearly see the waveforms differ in frequency (looking at values of Zeta from 0.1, 0.2, 0.3 etc)

Thanks

donpacino
Gold Member
Yes, I also understand that too. I guess the formulas I'm using are only valid for values up to zeta=1. I think that, what I'm currently studying only scratches the surface of this subject.
Why I've questioned this and because they don't just give you a value of Zeta, but also include a value of an I damped natural frequency wo. Why give both values to sketch a graph after all?

Are there any relationships between different values of Zeta, as you can clearly see the waveforms differ in frequency (looking at values of Zeta from 0.1, 0.2, 0.3 etc)

Thanks
you need zeta and the natural frequency to find the resonant frequency

Sorry a few typos above. Don't know how to edit.
Undamped natural frequency (wo)

donpacino
Gold Member
Yes, I also understand that too. I guess the formulas I'm using are only valid for values up to zeta=1. I think that, what I'm currently studying only scratches the surface of this subject.
Why I've questioned this and because they don't just give you a value of Zeta, but also include a value of an I damped natural frequency wo. Why give both values to sketch a graph after all?

Are there any relationships between different values of Zeta, as you can clearly see the waveforms differ in frequency (looking at values of Zeta from 0.1, 0.2, 0.3 etc)

Thanks
In general the relationship for zeta is exactly like you said. crit damped at 1, overdamped at less than one, and underdamped at more than 1

Ok, but how is that helping me sketch the graph [emoji53]

Ok, but how is that helping me sketch the graph [emoji53]

I estimated ζ=2 based on the graph in the notes, it's all i could think to do.

donpacino
Gold Member
Ok, but how is that helping me sketch the graph [emoji53]
like gneild said, you may be overworking the problem. If you really want to plot it, solve the differential equation and plot it

Hi Gneill. please can you take a look at my sketch and let me know if i am anywhere near?

Thanks

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gneill
Mentor
Hi Gneill. please can you take a look at my sketch and let me know if i am anywhere near?

Thanks
Take a look at the set of normalized curves presented on the wikipedia page: RLC Circuit

David J
Gold Member
I have no idea where to begin with this.

The question gives us:

a) ζ = 0.5, ω = 1×10^3 rad s^-1
b) ζ = 0.2, ω = 2×10^3 rad s^-1
c) ζ = 2, ω = 1×10^3 rad s^-1

The only thing i can find that relates ζ & ω is ζ = α/ω

a) α = 1000
b) α = 800
c) α = 4000

Apologies for digging up an old thread but I am trying to work out how you came to these answers above, namely ##\alpha = 1000##, ##\alpha=800## and ##\alpha = 4000##.

I get ##\alpha =500##, ##\alpha=400## and ##\alpha = 2000## respectfully. I am obviously wrong but could someone explain where I am going wrong with this please ??
thanks

donpacino
Gold Member
Apologies for digging up an old thread but I am trying to work out how you came to these answers above, namely ##\alpha = 1000##, ##\alpha=800## and ##\alpha = 4000##.

I get ##\alpha =500##, ##\alpha=400## and ##\alpha = 2000## respectfully. I am obviously wrong but could someone explain where I am going wrong with this please ??
thanks

Your alpha values and Gremlin's alpha values seem to have a constant relationship with each other.
Maybe you should look into how you did it, and what the equation is.

Hint... what do you have to do to change all of your answers to match Gremlin's?

David J
Gold Member
Yes, the constant relationship is that my values are 50% of his values so for my values to be correct I need to multiply by 2 but I cant seem to see why. I just re arranged the equation below but it didnt work out.

"The only thing i can find that relates ζ & ω is ζ = α/ω"

I cannot see where the X 2 is required unless I am missing something to do with the "rad s^-1" which is common to all of the ##\omega## values

Reading these threads I am still lost at how the natural frequency fits in with the sketch of the waveforms.
I understand the shapes of the curves from damping ratio but struggling with the significance of the frequency.
Looking through my notes I can see the natural frequency has a great importance in the differential equation but can't relate it to the graph :-(