Frequency Response 

Thanks. I am glad you liked my visualization.

How is this abstract when you can literally plot bode on an oscilloscope or in matlab and clearly see it?

@@RazvanGabor Greetings, it is the math itself which is abstract, since it relies on logic and theorems. Coincidentally, it very well explains many of the things and behaviors that happen or exist in real life, such as the way a system responds to frequency in this case. The matlab library that plots frequency response probably uses an algorithm that employs the fourier transform itsef somehow. In terms of measuring equipment, oscilloscopes (amplitude vs time) and spectrum analyzers (amplitude vs frequency) use complex circuitry to sample and then plot these things. Hope that helps. Cheers 🍻

@@RazvanGabor psst: that’s still abstract

Omg.same here. this would have made a huge impact on my life if i saw it 10 years back! Even life decisions:/

If i had a time machine and could go back even 25 years to college i could Ace any test with this type o info.

Im 29 and also couldnt agree more

I hear you. Unfortunately with or without internet there still are a lot of teachers out there that puts out the thirst for knowledge.

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-i3560RBklL0.html

Thanks for that really great compliment.

@@EugeneKhutoryansky welcome!!

No doubt about that. Since I'm a proponent of Everett's interpretation of QM, I cannot help but pity that other me who never found that channel....

@@ChaineYTXF which other channels do u recommend and which do u think are gems?

@@bk-sl8ee Hello. Depending on your level and the languages you speak, there are several in math and physics which I happen to enjoy: - Frederick Schüller (German lecturing IN ENGLISH in Physics and math for physics grads, working at the perimeter institute) - Pavel Grinfeld's MathTheBeautiful channel, and his books. Vectors, tensors, with AND without coordinate systems - BlackPenRedPen for quick problems in math (integrals, sequences, series, complex numbers, differential equations) - Leonard Susskind's lectures at Stanford - Walter Lewin's own. He has a true pedagogical talent and the lectures are quite entertaining. He's the real life Dr "Doc" Emett Brown from Back to the Future, if you know the movies (the movie character is not inspired by him but.. the character is very close to lewin) - Michael Penn for maths, he proves almost everything, very good stuff. - (In French) Etienne Parizot (Math for Physics, Special Relativity, Quantum mechanics) - (In French) Electronics, classical mechanics (no Lagrangian or Hamiltonian): "E-Learning Physique" from a professor at a reputed institution. - (in German) "Urknall Welt und das Leben" channel and especially its series "Von Aristoteles zur String Theorie" with calculations and insights provided by theoretical Physicist Josef Gaßner Then, books😁 I'd like some input from other people if possible if you have interesting channels in: - classical electrodynamics (up to antennas included) - electronics - nuclear physics - particle physics - theoretical lectures on black holes - quantum electrodynamics Any help would be much appreciated How my answer helps refine your choices of teachers on YT😊

Thanks for the compliment.

@George gabriel as well as the best channel in terms of properly understanding the knowledge of said fields through rigorous philosophical application and interpretation. This channel is truly a blessing and amazing to be able to deal with very difficult concepts from very different disciplines; from the hard sciences, to the different mathematical and analytical logic/languages that describes these hard sciences, through philisophical metaphysical and epistemoligical implications/understandings of said phenomena and synthesize them together quite neatly in order to present a comprehensive and cohesive understanding of the nature of our reality, and then presents said almost often unintelligible material (although also demonstrates a mastery level of said material) quite nicely through very easy to understand presentations for the layman without compromising accuracy and truthfulness of the material.

@@12345shushi I appreciate 👍

Can confirm. Some videos have an enormous replay value, in an unlikely event of one becoming smarter few years later. Unlike the latest video about some smartphone that is outdated one week after

Thanks for the compliments.

I am glad my videos are helpful. Thanks.

Thanks for the compliment. I am glad my videos are helpful.

Thanks.

Thanks. I am glad my video came out just in time for your exam. Good luck with it.

Thanks for the compliment about my videos.

Thanks.

Thanks for the compliments.

Thanks.

Thanks.

Thanks.

Thanks. I am glad you like my videos.

Thanks. More videos are on their way.

Thanks. I am glad my visualizations are helpful.

Thanks. I am glad my video was helpful.

I plan to do additional videos on control theory in the future. Thanks.

Cool. I did chem engineering and control theory was one of the most challenging bits for me

Thanks for the compliments.

@@EugeneKhutoryansky Thank you ...😊

Thanks for sharing the link to my video and I am glad that it is helpful.

I am glad my video was useful.

Thanks. I am glad that you like my videos.

Thanks for the compliments. I am glad you like my videos.

Thanks. Glad you liked it.

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@@EugeneKhutoryansky I thought it was "Frequent Questions"

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I am also happy you found my channel. Thanks.

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I am glad my video was helpful. Thanks.

Thanks for the compliment.

Thanks.

Thanks. I am glad you liked my video.

Thanks for the compliment about my video. I already have a few videos on Control Theory. The links are at the end of the video.

Thanks. I am glad you like my videos.

“Like” is too weak a term. “Am grateful for” is a little closer. Becoming a Patreon as soon as I finish typing this. You are doing unmitigated good for the world

Thanks. I really appreciate your support!!!

Yes same case with me.

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Thanks.

Thanks.

Thanks.

Thanks. Though, the spring will still be OK at the resonant frequency if there is sufficient damping to the system, as in the original example.

@@EugeneKhutoryansky Oh 😳 you mean to say that even at the resonant frequency, it is not necessary that the system will be damaged. Only the amplitude is maximum at resonant frequency; breaking of the system is an exceptional case?

Yes, the amplitude is a maximum at the resonant frequency, and whether or not the system will break depends on whether or not it can handle this amplitude. If there is no damping, then the amplitude at the resonant input frequency would theoretically reach infinity.

@@EugeneKhutoryansky What is spring?

@@EugeneKhutoryansky Wow. 😱😱 Thank you very much my mentor for giving me this precious conceptual sentence . "If there is no damping in the system, the amplitude at the resonant input frequency will theoretically reach infinity." 💖💖💖💖💖💖💚💚

Thanks.

Thanks.

@@EugeneKhutoryansky my pleasure

I make my 3D animations with "Poser." Thanks.

I will add that to my list of topics for future videos. Thanks.

Thanks for the compliment. I make my 3D animations with "Poser." Though, Poser does not have built in functions for complex variables. I had to create those myself.

To calculate the frequency response, we enter s = (i)(w). This will have the highest amplitude where w is equal to the imaginary component of one of the poles, and w is equal to 2*pi*frequency.

@@EugeneKhutoryansky so you mean pole won't have real component ,only imaginary component s=iw ?

The pole can have both a real component and an imaginary component. But, the frequency response is at a maximum when (i)(w) is equal to the imaginary component of the pole.

@@EugeneKhutoryansky I am confused in s=iw part. I can understand that as 50 Hz sine input can be represented as s=iw .but in what kind of input we represent with real part(x) of s=x+iw

The pole can have both a real component and an imaginary component. But, the frequency response is always H(iw), which is at a maximum when (iw) is equal to the imaginary component of the pole. We first calculate w = 2*pi*frequency, and then we calculate the transfer function H(s) at s= (iw).

Thanks for the compliment about my video. I make my 3D animations with Poser. I discuss how I make my 3D animations in my video at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-6Hl5dvA88Uo.html

I make my 3D animations with "Poser." Though, Poser does not have any built in functions for complex variables. I had to write those myself. Thanks for the compliment.

Glad to hear that.

The transfer function is always symmetric across the real axis, for any system that can actually be physically implemented.

Thanks for the compiment. I have a detailed video on waves at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Io-HXZTepH4.html

I make my 3D animations with "Poser." Though, Poser does not have built in functions for complex variables. I had to create those myself.

Thanks.

"s" is the frequency parameter, so Im(s) is the frequency. Re(s) is, well, the imaginary frequency, so exp(st) has both oscillatory and exponential behavior. The springs were all the same, with resonant frequency squared f^2=k/m, and damping ratio "g". The transfer function then goes like 1/sqrt( (2fg)^2+ (f^2-s^2)^2/s^2)

I explain Kirchhoff's Laws in my video at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-m4jzgqZu-4s.html I explain Maxwell's Laws in my video at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-9Tm2c6NJH4Y.html

@@EugeneKhutoryansky Thank you!

All the music in this video is from the free RU-vid audio library, and the names of the songs are the following. Wedding_Invitation Wigs Fur_Elise_by_Beethoven

Glad my video was helpful. Thanks.

I cover that in my video on imaginary numbers and functions of complex variables at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-bIY6ahHVgqA.html

No, the real part of s is not omega. We first calculate w = 2*pi*frequency, and then we calculate the transfer function H(s) at s= (i)(w). In other words, we calculate H(iw). The output of this gives a complex number with a magnitude and a phase. Thanks.

First I would like to correct myself: 1:43 clearly shows that what I was referring to is the imaginary part and not the real part. I just thought it was omega because 1:27 said so. It suggested to me that changing the frequency would only move on that line, change the imaginary part of the input. So I thought that if changing the frequency can't move the input in the direction of the real component, what parameter other than the frequency would I have to change to get to those massive magnitudes that aren't on the original line? Maybe something about the mass, the stiffness of the spring, or the damping?

If we reduce the damping to zero, then the two locations where the magnitude is infinity will be on the imaginary axis, and it will be possible to pick a frequency such that |H(iw)| = infinity.

Yes, it is a regular transfer function graph. I am showing the relationship between the transfer function and the frequency response. Thanks.

I cover resonance in RCL circuits in my video at ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-Mq-PF1vo9QA.html Thanks.

I make my 3D animations with "Poser."

Yes.

Those answers are not answerable by physics, it's really more philosophy. Either way, you would probably be more interested in a channel like Arvin Ash to answer those questions.

It relates to many applications i.e being studying mechanical engineering, I am gonna use this concept to prevent the parts of machines to break or fail due to mechanical vibrations. I hope you got it.

Not an engineer here. But doesn’t this concept explain why the infamous Tacoma Narrows bridge collapsed. The wind being the input frequency and the “gallop” of the bridge being the output frequency? So the engineering mistake was not accounting properly for the transfer function? Anyone can help me here?

David, yes you are basically correct. To be more precise, the wind created an input function which included frequency components at the resonant frequency.

@@Pseudify Yes you are right. They forgot to take the wind into account. You must have noticed that when high speed winds flow, they don't keep on flowing. The first high pressure wind slap move the bridge from its mean position to one extreme position, after that slap of wind the pressure suddenly drops down and the bridge moves (oscillates) to its other extreme position. I mean to say that like sound waves, winds also flow like waves, i.e, in the form of compressions and rarefactions of large wavelengths. I hope you got it. The solution to your problem is to simulate the wind analysis for that bridge. Thank you.

Thanks.

I make my 3D animations with "Poser." Though, Poser does not have built in functions for imaginary numbers and complex variables. I had to create those myself.