JuddJones
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Posted 1551217166
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#1
I am working on the Mobius Level 4 training and am having a difficult time grasping the real vs imaginary concept as it applies to vibration. Does anyone have a resource (good you tube video, a calculus for dumb millwrights book, etc...) to help me grasp this? Or if you are the perfect resource to explain this in a way a hammer swinger can understand I would much appreciate it.

John from PA
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electricpete
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Posted 1551273395
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#3
A single scalar number maps along one dimension. We could consider the result a 1-d vector. What if you are trying to represent a 2-d vector (such as one that includes magnitude and phase)? Then you need two numbers. You could write them as an ordered coordinate pair (x,y) = (a,b). Or you can write them as a complex number which is a sum of real and imaginary components: a + i*b (this is the rectangular form of the complex number). We can convert the rectangular form a + i*b into a polar form R*exp(i*theta) using a little geometry and taking advantage of Euler's formula. R is the magnitude of the vector and theta is the phase. Complex numbers are primarily used as an easy way to manage 2-d vectors and vector arithmetic. What exactly the vectors represent can vary depending on what you're doing. https://en.wikipedia.org/wiki/Complex_number#Visualisation

weller
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Posted 1551275467
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#4
This might help with the Calculus........ http://www.gutenberg.org/ebooks/33283

Shurafa
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Posted 1551278813
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#5
Big J, Good luck with your course. Can you please specify in which topic you see these terms? Real and imaginary numbers have many applications. I'm not good in math but maybe the forum members can help better if you give more details. Is the topic related to the transfer function? Regards- Ali M. Al-Shurafa

John from PA
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Posted 1551280939
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#6
Quote:

Originally Posted by Shurafa Big J, Can you please specify in which topic you see these terms? Regards- Ali M. Al-Shurafa

The OP does state "Mobius Level 4 training" and the content is covered well at https://www.mobiusinstitute.com/site2/detail.asp?LinkID=23 . One thing listed, and likely where real/imaginary is covered is the content relative to " Advanced signal processing."

JuddJones
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Posted 1551281702
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#7
Thank you everyone.. This forum never disappoints. John is correct, it is covered extensively in the signal processing section. Currently I am in the system dynamics section where it is being discussed in relation to representing complex data (bode, nyquist, etc...). I had a light bulb moment yesterday in relation to this. I had been thinking of it purely in terms of numbers (and in 1D on paper), and hadn't grasped the "more than one axis to the math world concept" (similar to Electricpete's response). 3d animations help me a great deal. I came across a video that had some good 3d animations of modeling sin waves. Something clicked. When I am learning difficult (to me) concepts it sometimes feels like I shut off 40% of my brain. To be honest, I don't have the math skills necessary for a lot of this content. That won't stop me though, I have time.

Shurafa
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Posted 1551297976
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#8
Well, I didn't not take Mobius course. I wish to take it one day .System dynamics and signal processing are (in my understanding) different but yes both may use complex numbers. Transfer function is a concept that is applied in both subjects and in others like complex balancing. It's diving output signal over input signal (i guess) and this can result in real and imaginary numbers. Sometimes real and imaginary numbers are possible to think of as numbers in a plane of x and y axes. So, in a very simplified example, if you apply a force on a rotor in the horizontal direction it moves in the horizontal direction. But if it moves in both horizontal and vertical directions then there is a cross effect and here comes the concept of complex numbers. Damping is sometimes considered as an imaginary quantity because it works with shaft velocity vibration compared to shaft displacement vibration. Velocity is 90 deg away from displacement or at the y axis compared to x axis.I hope I'm not mixing things up now. But for someone studying for a certification exam I assume I need to perform some calculations like vectors addition and conversion from a coordinate system to another. Please let us know more about what example in the course if you don't mind. Regards- Ali M. Al-Shurafa

Walt Strong
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JuddJones
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Posted 1551302387
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#10
Thank you!

Shurafa2
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Posted 1551630159
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#11
I've done a quick review and search on the imaginary numbers in signal processing related to our field. Below are some of the key points:

In Bode pot, the real part is the amplitude. Imagery part is the phase angle.

Similar plots to Bode (response functin of an imact test) use also real and imaginery numbers.

Recall: 2^2 =4, (-2)^2 = 4, sqrt(4) = 2 or -2. All of these are real numbers. Imajeinary number i is crzy, i^2 = -1. Regards- Ali M. Al-Shurafa

OLi
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Posted 1551683209
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#12
In my book the Bode plot is a amplitude/phase plot https://en.wikipedia.org/wiki/Bode_plot https://en.wikipedia.org/wiki/Bode_plot So it is the other representation of the Re / Im data, Re/ Im is the X, Y coordinates in like a polar plot, Bode represent the same data but in amplitude and phase representation so it is the same data but Im is not a phase in degree's and is not a phase like that it is a number just like Re or X and Y in polar plot or what you may call it. Imaginary are funny guys but handy and you can do a very efficient 1-plane vector balance calculation using that system.

__________________ Good Vibrations since early 1950's, first patented vibrometer 1956 in the US.http://www.vtab.se