Sketch waveform to represent the transient response

[donpacino]

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

 

[Electest]

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

 

[Gremlin]

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]

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

 

[Hndstudent]

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

Thanks

 

[gneill]

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]

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]

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]

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 can't 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

 

[MattSiemens]

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 :-(