What a great professor.......he uses examples to show natural frequencies of various objects and then mathematically explains it. Vibration expertise is very important to Engineering but is very difficult to learn. You must do many problems before it "clicks".
Angela Hall God is required dear. Where the hell this complicated brain machine has come from? From nowhere if sorry you need to revisit your common sense.
I am currently studying a mechanical engineering course in the uk and this video saved me on my CW when it comes to damped vibration and the experimental data analysation. amazing video keep doing what you love
Professor Vandiver, thank you for an incredible lecture on the Introduction to Mechanical Vibration. Mechanical Vibration is a very important third year class for Mechanical Engineering students. All students majoring in Mechanical Engineering should master these concepts before taking Mechanical Vibrations.
I agree with Dr. Vandiver up to a point. The kinetic vibration from a K1 and K2 facilitated solution has to be met with proper centrifugal force applied properly. I am excited with the new development of Euler's Formula to prove true kinetic energy displacement. MIT has allowed me to broaden Euler's Formula and has allowed me to truly invent the way kinetic motion through displacement exists. This will actually be covered in my theses. 7.5 years at MIT and I am finally starting to visualize the light at the end of the tunnel.
I really needed this. I'm taking structural dynamics this semester and the first lecture I received was a 3hr class that lecturer didn't stand up once to explain anything. He sat through the whole class and read from his slides. Thank you for this
Just stumbled on this while working on a dynamic balancer. I hadn't seen this good of a simple derivation of spring, mass, dashpot in years. It flowed nicely like an old song and warmed the cockles of my heart. Stu Fields BSEE
That is the better way to explain all Mechanical Vibration basics I've never seen. Fine, such a fantastic Lecture! Isn't it? Right now, seeking the complete course...
When I was in college, my lecturer missed dynamic part. It is very important and hence useful topic for practice engineers alongside with Fourier transform. Excellent lecture ! I am learning this part.
After seeing the quality of the instruction in these courses I understand why it means something different to go to these schools - compared to my 100% acceptance local engineering university... for a professor to exhibit this level of organization, eloquence, and lucidity is truly something special... would be fantasy at ATU...
In reality there’s only one way mechanical vibration works. Sadly if you were taught otherwise it was just incorrect. Some people are better at explaining to the masses than others but the solutions should be exactly the same.
@williambradley835 Yes, I mean that the quality of this explanation is much higher than any that I ever received at my university. Of course, the engineering is the same, but instead of learning it from lectures we mostly had to teach ourselves!
please solve this Mcqs Thank you. 1) All vibrating bodies have following Degree of Freedom: a)1 b)2 c)3 d)4 . 2) The frequency of vibrations with increase of damping in the case of free vibrations with coulomb damping will A.Remain the same B.Increase C.Decrease D.May increase or decrease depending upon the damping coefficient
Some of the greatest examples of vibration that people can relate to are tires out of balance and spinning washing machines out of balance..... Your shocks or struts in your car are dampers that absorb forcing functions such as potholes or seams on the freeway and hopefully keep you away from the natural frequency.
cuz in a static analysis there is no motion, therefore no velocity and no acceleration so both x double dot and x dot are zero. which means (k1+k1)xs=l/2(k1-k2)
@@damianblandi4294 When ignoring the dynamic forces, (k1+k2)xs=l/2(k1-k2), which means when plugged back into the equation involving dynamic forces, you can cancel like terms. Think of "(k1+k2)xs" and "l/2(k1-k2)" in terms of a variable "x". if you were to rewrite the equation in terms of this new variable "x", you could subtract x from both sides and cancel them out resulting in cero.
Damn...it's been like 20 minutes into the video and I'm completely lost but surely entertained. I am a mechanical drafter but I'm considering going back to school for mechanical engineering and this is like Chinese to me lol. The hardest level of math I completed was trig and algebra 3. I thank this man for sharing his knowledge, so awesome :)
Jesus Carrillo that is probably why you can't get it. Iam currently coursing mechanical engineering and this subject belongs to my sixth term. Of course you don't get it, hahaha.
physical intuition of damping ratio (i.e. less the damping ratio doesnot mean it will vibrate for more time, it's actually take more number of cycles to decay the vibration amplitude) is lit
at 1:02:09 added mass is not the correct reason for that because gravity works independent of mass.specially in case of simple harmonic motion. it may be resistance offered by water that is may be drag force. i think so
I am really grateful for this content. It allows me to learn so much. Thanks you so much, MIT. I really appreciate it. I believe there's a "issue" in one of the equations. When the professor analyses the value of s for values of etha bigger than 1. I believe he misses a factor of w in the second term of s. 47:33
Having problems with vibration. Comes from downstairs a apartment below me. I dont know how or why and my manager of the apartment can't help unless I can prove my point. So I am interested in any thing have to with vibration and how its cause and why someone use it and how they can make vibrates/Vibrations upstairs. HELP PLEASE
How can you hold the professor up to impossible high standards? He makes a small mistake and you think it is unacceptable? You may want to change your attitude and accept everyone makes mistakes no matter who they are.
hugh jorgan haha lol he will be like “ but sir the resonance is false using my knowledge as I’m truly smart I know that you are wrong as using my scientific mathematical brain I have created a new form of a new species using electronically structured material to then drown in a heated lake until I have made an alien from mars” I don’t know what I said but merry Christmas man
Sheldons are there.....I met a few in Engineering classes......I was an A- B student in these level of classes.....some guys could work months ahead in the book.....prodigies.
I think it's because xs is the displacement of the block in the static condition, meaning it's not dependent on time. This makes it a constant. Left and right side of the equation are equal meaning they can both be subtracted out of the equation.
There are no required textbooks for this course, but suggested readings are drawn from the following texts: [Hibbeler]= Hibbeler, Russell C. Engineering Mechanics: Dynamics. 12th ed. Prentice Hall, 2009. ISBN: 9780136077916. [Williams]= Williams, J. Fundamentals of Applied Dynamics. John Wiley & Sons, 1995. ISBN: 9780471109372. See the course on MIT OpenCourseWare for more info and materials at: ocw.mit.edu/2-003SCF11. Best wishes on your studies!
How could I obtain the relevant acceleration by taking into account the Fourier transform? Because if you use the Simple Harmonic Motion, acceleration will always increase as frequency increases. In reality, structures are affected by certain frequency. So, how can I consider both the peak acceleration and the frequency in which my structure will have resonance effects?
Same here, I am in 9th and im soo confused and I want to become an engineer but this scares me! Makes me doubt whether I want to do it coz I was just blank
@@cult4037 Bro, you’re only in 9th grade chill out. You’ll be fine, don’t stress about this. This is an MIT lecture. Just keep your grades high and take the hardest level math and science courses available at your school. Pass those. If you enjoy the pain by then, you’ll be a great engineer.
Why'd he use a dice? There are no dice.... e{a}/t=hv. A 5th above is a 4th below. So... can I put a KK2 controller board right next to the motor if I balance my prop with the motor? That's what I need to know before the operation..... Mass spring dashpot... I'll try to remember that term. Sounds important;-)
Why aren't there lectures for 2.004, Dynamics & Control II, MIT OCW? So many course on OCW for Mechanical Engineering lack lectures...many courses lack lectures. Wish it would get filled up.
The main reason is money. MIT contributes 1M+ every year to MIT OpenCourseWare. Even with that funding, we are only able to record a limited number of full courses each year (~12 courses). We try and prioritize which courses we can publish by a number of factors. Unfortunately, 2.004 has not made the video lists. Maybe sometime in the future we will get funding and time to recording 2.004. We do have materials for 2.004, just not videos: ocw.mit.edu/courses/mechanical-engineering/2-004-dynamics-and-control-ii-spring-2008/. Best wishes on your studies!
Hi I'm a autistic man with sensory difcultuys is there anyone who understands low frequency and vibrashion, I'm having difficulty with both, iv made a you tube Ja play, to show the vibration and app picking up the noise, i hope it's ok to ask. Thank you Jason
Wow I can't find a video now thay I can't find on sysmic vibrations and in hand with mechanical vibration but I'd like to hear your side on the matter I please sir
Im sure im farr off but this interests me alot and another thing I couldn't find o. Now is the proof behind rythmic or Marconi vibrations either man made or by a machine online anymore why is that because is dangerous I bet if we all timed a human wave across the planes it would have some kind of recourse and in other aspects jumping in a harmonuos succession could actually cause a problem
But if we all planned to jump at the sMe time on a grand scale it could do something of every human on the wold held it of one minute who who knows what it would do
I'm shocked that a professor at MIT makes such a mistakes! k1 × 𝛿1 = k2 × 𝛿2 𝛿1 + 𝛿2 = L ⇒ 𝛿i = ki × L / (k1 + k2) defining 𝛿 as 𝛿 = 𝛿2 - 𝛿1 then equation of motion is m × a = (k1 × 𝛿1 - k2 × 𝛿2) - (k1 - k2) × x where a is acceleration, the second time derivative of x at the middle. could it be any easier?
i feel like i am stupid cause i do not get most of his jumping from one concept to another. i mean he did explain a few things good but as a 19 year old i do not get him at all. I am scared at what would i have to learn in my future engineeering classes.
The world isn’t here to satisfy you. The world doesn’t owe you anything. If you can’t hack it, maybe consider a vocation that doesn’t require this level of brain power. You may not be able to handle it.
Respect to the camera/sound crew! Very well recorded and filmed!
What a great professor.......he uses examples to show natural frequencies of various objects and then mathematically explains it. Vibration expertise is very important to Engineering but is very difficult to learn. You must do many problems before it "clicks".
Welcome everyone, the algorithm has brought us together once again
이거 맞지
Curiosity brought me here.
I searched for it.
I just searched it but hi!
Welcome
This is really a perfect introduction to vibration theory, Prof. Vandiver really made it easy to digest! Strongly recommend this to you all.
Fuck this explanation bcoz this is not modify vibration
It is very satisfying to hear the sound the chalk piece makes with the blackboard.
A key part of what makes the MIT lectures so great to watch
Thank God for people likethis lecturer!! Proud to be an Engineer! !
No God required! That is the beauty of it!
th-cam.com/video/CS1b4nJo2Gw/w-d-xo.html
Elvis Charles th-cam.com/video/T2NyJmi5c7s/w-d-xo.html
@@angelahall4402 god req for everything
Angela Hall God is required dear. Where the hell this complicated brain machine has come from? From nowhere if sorry you need to revisit your common sense.
Watched the whole class, would like to applaud for great refresher of stuff learned 30 years ago.
Thanks for uploading.
I am currently studying a mechanical engineering course in the uk and this video saved me on my CW when it comes to damped vibration and the experimental data analysation. amazing video keep doing what you love
Hi
Professor Vandiver, thank you for an incredible lecture on the Introduction to Mechanical Vibration. Mechanical Vibration is a very important third year class for Mechanical Engineering students. All students majoring in Mechanical Engineering should master these concepts before taking Mechanical Vibrations.
So far, one of the best lectures of the course, very good.
I agree with Dr. Vandiver up to a point. The kinetic vibration from a K1 and K2 facilitated solution has to be met with proper centrifugal force applied properly. I am excited with the new development of Euler's Formula to prove true kinetic energy displacement. MIT has allowed me to broaden Euler's Formula and has allowed me to truly invent the way kinetic motion through displacement exists. This will actually be covered in my theses. 7.5 years at MIT and I am finally starting to visualize the light at the end of the tunnel.
Amazing lecture. Really explained the mathematical ground-work and the physical meaning behind it.
I really needed this. I'm taking structural dynamics this semester and the first lecture I received was a 3hr class that lecturer didn't stand up once to explain anything. He sat through the whole class and read from his slides. Thank you for this
I feel like the school should teach mechanical vibration before quantum mechanics, since it helps a lot in understanding the wavefunction
💯
Really nice explanation. Thanks, from India!
Just stumbled on this while working on a dynamic balancer. I hadn't seen this good of a simple derivation of spring, mass, dashpot in years. It flowed nicely like an old song and warmed the cockles of my heart. Stu Fields BSEE
Que lindo, qualquer pessoa no mundo poder te a oportunidade de assistir aulas direto do MIT, como eu, aqui em uma pequena cidade do Brasil.
Pacho, Pacho!
That is the better way to explain all Mechanical Vibration basics I've never seen.
Fine, such a fantastic Lecture! Isn't it?
Right now, seeking the complete course...
When I was in college, my lecturer missed dynamic part. It is very important and hence useful topic for practice engineers alongside with Fourier transform. Excellent lecture ! I am learning this part.
thank you for the lectures! Really enjoyed this one, even though it took me about two hours to get through it
greetings from TUL, Czech Republic
After seeing the quality of the instruction in these courses I understand why it means something different to go to these schools - compared to my 100% acceptance local engineering university... for a professor to exhibit this level of organization, eloquence, and lucidity is truly something special... would be fantasy at ATU...
In reality there’s only one way mechanical vibration works. Sadly if you were taught otherwise it was just incorrect. Some people are better at explaining to the masses than others but the solutions should be exactly the same.
My third world university is shit, full of low IQ professors that don't know the subject. The difference of this class and my college is extremely big
You mean Accra Technical University?
@@steveyorke1230 Nope, Arkansas Tech University
@williambradley835 Yes, I mean that the quality of this explanation is much higher than any that I ever received at my university. Of course, the engineering is the same, but instead of learning it from lectures we mostly had to teach ourselves!
this is why this school is called MIT, thanks professor
Its really fantastic & i am very much convinced with the approach used to find out the critical damping. Thanks a lot for such a great lecture sir.
please solve this Mcqs Thank you.
1) All vibrating bodies have following Degree of Freedom:
a)1
b)2
c)3
d)4
.
2) The frequency of vibrations with increase of damping in the case of free vibrations with coulomb damping will
A.Remain the same
B.Increase
C.Decrease
D.May increase or decrease depending upon the damping coefficient
1:07:59 should have been (n)(zeta)(omega n)(tou d)
Rest the video is awesome, this is not much of an error, just in case someone finds it confusing
Some of the greatest examples of vibration that people can relate to are tires out of balance and spinning washing machines out of balance.....
Your shocks or struts in your car are dampers that absorb forcing functions such as potholes or seams on the freeway and hopefully keep you away from the natural frequency.
I need more lectures on Mechanical Engineering. Eng. Dynamics are good but I need others too!
Your simplifying how far it goes on a grand scale
16:48 Why are they equal?
cuz in a static analysis there is no motion, therefore no velocity and no acceleration so both x double dot and x dot are zero. which means (k1+k1)xs=l/2(k1-k2)
plug in ks
@@Romulo_Cunha but why is it cero? I mean why do they cancel each other in that ecuation?
@@damianblandi4294 When ignoring the dynamic forces, (k1+k2)xs=l/2(k1-k2), which means when plugged back into the equation involving dynamic forces, you can cancel like terms. Think of "(k1+k2)xs" and "l/2(k1-k2)" in terms of a variable "x". if you were to rewrite the equation in terms of this new variable "x", you could subtract x from both sides and cancel them out resulting in cero.
He calculated Xs one step before, then you just substitute Xs now for the static case and you will see
great resource keep it up MIT
Damn...it's been like 20 minutes into the video and I'm completely lost but surely entertained. I am a mechanical drafter but I'm considering going back to school for mechanical engineering and this is like Chinese to me lol. The hardest level of math I completed was trig and algebra 3. I thank this man for sharing his knowledge, so awesome :)
Algebra 3? Do you mean precalculus?
Jesus Carrillo that is probably why you can't get it. Iam currently coursing mechanical engineering and this subject belongs to my sixth term. Of course you don't get it, hahaha.
Haven't a clue what he's talking about ,
But he makes it sound interesting 🤔
Thank you very much Professor and MIT service.
VERY GOOD VIDEO, MAKE ME CAN EASY TO CALCULATED Mechanical Vibration.
+Logxn 😂😂
Jakobus Rante th-cam.com/video/T2NyJmi5c7s/w-d-xo.html
This was awesome. Thank you. Very straightforward explanation of the basics.
Ich brauche mehr Vorträge zu vielen Themen, bitte
This video is the reason that I finally learnt damping . Thank you so much!
physical intuition of damping ratio (i.e. less the damping ratio doesnot mean it will vibrate for more time, it's actually take more number of cycles to decay the vibration amplitude) is lit
Time delay is phi(phase angle) over omega n(natural frequency).
Step by step video solutions of civil engineering questions
at 1:02:09 added mass is not the correct reason for that because gravity works independent of mass.specially in case of simple harmonic motion. it may be resistance offered by water that is may be drag force.
i think so
Mass depends on gravity not vibration...ur explation is worng ...so u not perfect
This is a essential lessions for students from 16-18 years old in VietNam. Too hard to study in that age
Do you take in that much detail of calculus, I doubt it!
Imagine paying half a million dollars to go to one of the best schools in the world, then they post all your lectures on youtube.
Will Hunting "You dropped a hundred and fifty grand on a education you could've gotten for a dollar fifty in late charges at the public library."
They are all free anyway. You just need to borrow text books which explain in more detail from libraries.
It's the informatic age. Knowledge is no longer power. It's your brain and time that are valueable.
you pay for the certificate not the stuff ypu learn.
@@tumdeax Yup that's the movie
I am really grateful for this content. It allows me to learn so much. Thanks you so much, MIT. I really appreciate it.
I believe there's a "issue" in one of the equations. When the professor analyses the value of s for values of etha bigger than 1. I believe he misses a factor of w in the second term of s. 47:33
Juan Manuel Garcia th-cam.com/video/T2NyJmi5c7s/w-d-xo.html
Really nice videos! Congratulations!
Anyone else still in high school just midway through AP calculus and AP physics 1 and have no idea what he’s talking about?
8th grade hoping to get there.
Having problems with vibration. Comes from downstairs a apartment below me.
I dont know how or why and my manager of the apartment can't help unless I can prove my point. So I am interested in any thing have to with vibration and how its cause and why someone use it and how they can make vibrates/Vibrations upstairs. HELP PLEASE
EXCELLENT TOPIC WHAT IS RECOMENDED VIBRATION LEVEL FOR A PUMPS ,
This knowledge must have been a holy grail to ancient people (and also to some of us). How do you compute Q from the damping ratio?
“This is just the basic intro to 2004”
Omfg.
32:08 the inverse tangent should be (w_n*x_0)/(v_0), isn't it?
wow ...the basics have been taught very nicely
But what does that have to do with the price of tea in china
thanks for improving of engineering knowledge
This was absolutely wonderful and helpful. Many thanks for sharing this video.
Great lecture but at minute 48:38, there is an omega term missing after the plus and minus. isn't it?
+Warsame Cabdillahi he's human after all and we do mistakes
+Youcef Mahdadi Not really acceptable when ur a teacher of the field... Especially if ur a prof at the worlds best university...
How can you hold the professor up to impossible high standards? He makes a small mistake and you think it is unacceptable? You may want to change your attitude and accept everyone makes mistakes no matter who they are.
I always imagine young Sheldon sitting in the front row for these lectures.
hugh jorgan haha lol he will be like “ but sir the resonance is false using my knowledge as I’m truly smart I know that you are wrong as using my scientific mathematical brain I have created a new form of a new species using electronically structured material to then drown in a heated lake until I have made an alien from mars” I don’t know what I said but merry Christmas man
Sheldons are there.....I met a few in Engineering classes......I was an A- B student in these level of classes.....some guys could work months ahead in the book.....prodigies.
i wish study in america really ...in my university there is not even a chair to sit on it
+Mohamed Laham wtf
+Djamila Dz bro it is the ugly truth
+Mohamed Laham THANK YOU:)
+Ho Hoang Tu :)
+Dung Le yeah man..google it by writing Fet university in jordan :)
he also teaches a class on comb overs.
thank you so much, you make more easier for me
Great explanation. thanks, from brazil!!!
How do the k terms in (k1+k2)xs= L/2(k1-k2) cancel out????? @ 17:12 ????????
I think it's because xs is the displacement of the block in the static condition, meaning it's not dependent on time. This makes it a constant. Left and right side of the equation are equal meaning they can both be subtracted out of the equation.
They're pushing with equal force in opposing directions, resulting in a net movement of zero.
Can anyone tell me what was that at 3:50
Hello
Could I get the book title used to support the course please
There are no required textbooks for this course, but suggested readings are drawn from the following texts:
[Hibbeler]= Hibbeler, Russell C. Engineering Mechanics: Dynamics. 12th ed. Prentice Hall, 2009. ISBN: 9780136077916.
[Williams]= Williams, J. Fundamentals of Applied Dynamics. John Wiley & Sons, 1995. ISBN: 9780471109372.
See the course on MIT OpenCourseWare for more info and materials at: ocw.mit.edu/2-003SCF11. Best wishes on your studies!
How could I obtain the relevant acceleration by taking into account the Fourier transform? Because if you use the Simple Harmonic Motion, acceleration will always increase as frequency increases. In reality, structures are affected by certain frequency. So, how can I consider both the peak acceleration and the frequency in which my structure will have resonance effects?
wonderful presentation
Me in middle school being confused af while watching this; 👁👄👁
Same here, I am in 9th and im soo confused and I want to become an engineer but this scares me! Makes me doubt whether I want to do it coz I was just blank
@@cult4037 Bro, you’re only in 9th grade chill out. You’ll be fine, don’t stress about this. This is an MIT lecture. Just keep your grades high and take the hardest level math and science courses available at your school. Pass those. If you enjoy the pain by then, you’ll be a great engineer.
@@Punicia honestly really good advice
Being a Machinist my experience with vibrations was with chatter on a part !
this is very good and super course of Basics Vibration.top prof.
Why'd he use a dice? There are no dice.... e{a}/t=hv. A 5th above is a 4th below.
So... can I put a KK2 controller board right next to the motor if I balance my prop with the motor? That's what I need to know before the operation.....
Mass spring dashpot... I'll try to remember that term. Sounds important;-)
Really great content. Thanks!
Why aren't there lectures for 2.004, Dynamics & Control II, MIT OCW? So many course on OCW for Mechanical Engineering lack lectures...many courses lack lectures. Wish it would get filled up.
The main reason is money. MIT contributes 1M+ every year to MIT OpenCourseWare. Even with that funding, we are only able to record a limited number of full courses each year (~12 courses). We try and prioritize which courses we can publish by a number of factors. Unfortunately, 2.004 has not made the video lists. Maybe sometime in the future we will get funding and time to recording 2.004. We do have materials for 2.004, just not videos: ocw.mit.edu/courses/mechanical-engineering/2-004-dynamics-and-control-ii-spring-2008/. Best wishes on your studies!
Hi I'm a autistic man with sensory difcultuys is there anyone who understands low frequency and vibrashion, I'm having difficulty with both, iv made a you tube Ja play, to show the vibration and app picking up the noise, i hope it's ok to ask. Thank you Jason
Wow I can't find a video now thay I can't find on sysmic vibrations and in hand with mechanical vibration but I'd like to hear your side on the matter I please sir
So this class is about vibrators?
merci monsieur pour ces cours
Im sure im farr off but this interests me alot and another thing I couldn't find o. Now is the proof behind rythmic or Marconi vibrations either man made or by a machine online anymore why is that because is dangerous I bet if we all timed a human wave across the planes it would have some kind of recourse and in other aspects jumping in a harmonuos succession could actually cause a problem
But if we all planned to jump at the sMe time on a grand scale it could do something of every human on the wold held it of one minute who who knows what it would do
Ca. You test my theory
I'm shocked that a professor at MIT makes such a mistakes!
k1 × 𝛿1 = k2 × 𝛿2
𝛿1 + 𝛿2 = L
⇒ 𝛿i = ki × L / (k1 + k2)
defining 𝛿 as
𝛿 = 𝛿2 - 𝛿1
then equation of motion is
m × a = (k1 × 𝛿1 - k2 × 𝛿2) - (k1 - k2) × x
where a is acceleration, the second time derivative of x at the middle.
could it be any easier?
I really enjoyed the lessons thanks teacher and I'll like to get your books and i don't know what to do so i can get them
TEACHERS ALL PAID NOW.
博士好深奥，作用力和反作用力以及动能加浮性防阻和速度无反作用力，，，。
对了，若从出発点到高空再順时針方向或逆时针方向呢?，以前，而直上测或斜上测从动能以及矩離上的时问点和动能上，顺时针或逆时针或钭右上或斜左上，，，??。
只剩控方向陣列以及接收発波原理了，，，博士太猛了，，，。
I gave up on this but what i know from the past this needs more work sir
Are all mechanical engineering courses this hard or is it just MIT?
what is the reasons of natural freq. ? and what is the energy is produce this freq. ??
Lectures about Lagrangian &Hamilton mechanics
We are all created by vibration! Everything is
I have a feeling you're not talking about string theory..
Is there some lactures on governor on mit? Pls share link...
i feel like i am stupid cause i do not get most of his jumping from one concept to another. i mean he did explain a few things good but as a 19 year old i do not get him at all. I am scared at what would i have to learn in my future engineeering classes.
The world isn’t here to satisfy you. The world doesn’t owe you anything. If you can’t hack it, maybe consider a vocation that doesn’t require this level of brain power. You may not be able to handle it.
MY INTELLIGENCE IS ABSOLUTE..
رَبّيَ يَوَفَقً الُجْمٌيَْع
Shift the angle
respond (1)
Is this for medical use?
I can finally afford to go to MIT
Thank you sir for your lecture
Excelente clase !!!! saludos
Hi Professor thank you for the information, I didn't get the clarity on Phase angle
Thank you very much for providng us with such a great lecture.
HEAVEN.
It is good lesson for me.
Great lecture