19. Introduction to Mechanical Vibration

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  • เผยแพร่เมื่อ 19 พ.ย. 2024

ความคิดเห็น • 411

  • @vladimirsviridov3329
    @vladimirsviridov3329 4 ปีที่แล้ว +52

    Respect to the camera/sound crew! Very well recorded and filmed!

  • @Edmund007013
    @Edmund007013 7 ปีที่แล้ว +37

    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".

  • @thesingleszonechannel1413
    @thesingleszonechannel1413 9 ปีที่แล้ว +300

    Thank God for people likethis lecturer!! Proud to be an Engineer! !

    • @angelahall4402
      @angelahall4402 7 ปีที่แล้ว +17

      No God required! That is the beauty of it!

    • @automd976
      @automd976 6 ปีที่แล้ว

      th-cam.com/video/CS1b4nJo2Gw/w-d-xo.html

    • @psnb2573
      @psnb2573 6 ปีที่แล้ว

      Elvis Charles th-cam.com/video/T2NyJmi5c7s/w-d-xo.html

    • @leojoy9347
      @leojoy9347 5 ปีที่แล้ว +7

      @@angelahall4402 god req for everything

    • @muhammadtariqomer4733
      @muhammadtariqomer4733 5 ปีที่แล้ว +6

      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.

  • @maxajames
    @maxajames 5 ปีที่แล้ว +19

    It is very satisfying to hear the sound the chalk piece makes with the blackboard.

  • @TheDemonofallMusic
    @TheDemonofallMusic 5 ปีที่แล้ว +292

    Welcome everyone, the algorithm has brought us together once again

  • @beichuanqi4508
    @beichuanqi4508 7 ปีที่แล้ว +18

    This is really a perfect introduction to vibration theory, Prof. Vandiver really made it easy to digest! Strongly recommend this to you all.

    • @vikaskuntal7177
      @vikaskuntal7177 6 ปีที่แล้ว

      Fuck this explanation bcoz this is not modify vibration

  • @dozog
    @dozog 6 ปีที่แล้ว +37

    Watched the whole class, would like to applaud for great refresher of stuff learned 30 years ago.
    Thanks for uploading.

  • @davidwroblewski7215
    @davidwroblewski7215 4 ปีที่แล้ว +5

    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

  • @lorklorkman7937
    @lorklorkman7937 8 ปีที่แล้ว +7

    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.

  • @stevenshum83
    @stevenshum83 5 ปีที่แล้ว +77

    I feel like the school should teach mechanical vibration before quantum mechanics, since it helps a lot in understanding the wavefunction

  • @georgesadler7830
    @georgesadler7830 3 ปีที่แล้ว +2

    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.

  • @ricardo4fun922
    @ricardo4fun922 6 ปีที่แล้ว +8

    So far, one of the best lectures of the course, very good.

  • @Phatheading
    @Phatheading 8 ปีที่แล้ว +7

    Amazing lecture. Really explained the mathematical ground-work and the physical meaning behind it.

  • @christophermeyers1
    @christophermeyers1 2 ปีที่แล้ว +11

    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...

    • @williambradley835
      @williambradley835 2 ปีที่แล้ว

      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.

    • @Estebanmeinca
      @Estebanmeinca 2 ปีที่แล้ว

      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

    • @steveyorke1230
      @steveyorke1230 ปีที่แล้ว

      You mean Accra Technical University?

    • @christophermeyers1
      @christophermeyers1 ปีที่แล้ว +1

      @@steveyorke1230 Nope, Arkansas Tech University

    • @christophermeyers1
      @christophermeyers1 ปีที่แล้ว +1

      @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!

  • @DanielRodrigues-wq1rl
    @DanielRodrigues-wq1rl 4 ปีที่แล้ว +5

    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.

  • @silentflexseismiccontrol228
    @silentflexseismiccontrol228 9 ปีที่แล้ว +7

    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...

  • @BoZhaoengineering
    @BoZhaoengineering 5 ปีที่แล้ว +7

    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.

  • @zywang2793
    @zywang2793 4 ปีที่แล้ว +1

    this is why this school is called MIT, thanks professor

  • @vkpots
    @vkpots 8 ปีที่แล้ว +1

    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

  • @chinyerenwankwo1245
    @chinyerenwankwo1245 6 ปีที่แล้ว

    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

  • @arnabbhattacharya1992
    @arnabbhattacharya1992 10 ปีที่แล้ว +23

    Really nice explanation. Thanks, from India!

  • @bmphil3400
    @bmphil3400 4 ปีที่แล้ว +2

    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.

  • @RuneScapeQuestMaster
    @RuneScapeQuestMaster 4 ปีที่แล้ว

    Your simplifying how far it goes on a grand scale

  • @RS9World
    @RS9World 11 ปีที่แล้ว +3

    I need more lectures on Mechanical Engineering. Eng. Dynamics are good but I need others too!

  • @opsorryyt
    @opsorryyt ปีที่แล้ว

    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

  • @8WT7W4RX
    @8WT7W4RX 10 ปีที่แล้ว +4

    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

  • @chaitanyasurepally8249
    @chaitanyasurepally8249 8 ปีที่แล้ว +5

    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.

  • @Carrillo17
    @Carrillo17 10 ปีที่แล้ว +12

    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 :)

    • @MrBulat1990
      @MrBulat1990 10 ปีที่แล้ว +5

      Algebra 3? Do you mean precalculus?

    • @grijwoww
      @grijwoww 7 ปีที่แล้ว +3

      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.

  • @flavioing1
    @flavioing1 ปีที่แล้ว

    Thank you very much Professor and MIT service.

  • @bharath_rbp
    @bharath_rbp 4 ปีที่แล้ว

    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

  • @zayeemshafiq1887
    @zayeemshafiq1887 2 ปีที่แล้ว +2

    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

  • @Anomander888
    @Anomander888 3 ปีที่แล้ว +1

    Haven't a clue what he's talking about ,
    But he makes it sound interesting 🤔

  • @MasterCivilEngineering
    @MasterCivilEngineering 4 ปีที่แล้ว +1

    Step by step video solutions of civil engineering questions

  • @aydagr3219
    @aydagr3219 5 ปีที่แล้ว +3

    This video is the reason that I finally learnt damping . Thank you so much!

  • @Borntowin894
    @Borntowin894 4 ปีที่แล้ว +1

    Ich brauche mehr Vorträge zu vielen Themen, bitte

  • @ziecbizi2975
    @ziecbizi2975 ปีที่แล้ว +2

    This is a essential lessions for students from 16-18 years old in VietNam. Too hard to study in that age

    • @EducationalYM
      @EducationalYM ปีที่แล้ว +1

      Do you take in that much detail of calculus, I doubt it!

  • @nafe2437
    @nafe2437 10 ปีที่แล้ว +11

    great resource keep it up MIT

  • @ranteraptorkiller
    @ranteraptorkiller 8 ปีที่แล้ว +6

    VERY GOOD VIDEO, MAKE ME CAN EASY TO CALCULATED Mechanical Vibration.

    • @gauravpangarkar
      @gauravpangarkar 8 ปีที่แล้ว

      +Logxn 😂😂

    • @psnb2573
      @psnb2573 6 ปีที่แล้ว

      Jakobus Rante th-cam.com/video/T2NyJmi5c7s/w-d-xo.html

  • @changethematrix
    @changethematrix 8 ปีที่แล้ว +1

    This was awesome. Thank you. Very straightforward explanation of the basics.

  • @benberlowitz6381
    @benberlowitz6381 5 ปีที่แล้ว +6

    Anyone else still in high school just midway through AP calculus and AP physics 1 and have no idea what he’s talking about?

  • @ayushgupta5061
    @ayushgupta5061 8 ปีที่แล้ว

    wow ...the basics have been taught very nicely

  • @JuanManuelGarcia_machine
    @JuanManuelGarcia_machine 10 ปีที่แล้ว +12

    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

    • @psnb2573
      @psnb2573 6 ปีที่แล้ว +1

      Juan Manuel Garcia th-cam.com/video/T2NyJmi5c7s/w-d-xo.html

  • @wandergrv
    @wandergrv 4 ปีที่แล้ว +1

    Really nice videos! Congratulations!

  • @jeffreyschmiedeck4254
    @jeffreyschmiedeck4254 ปีที่แล้ว

    Being a Machinist my experience with vibrations was with chatter on a part !

  • @Civil.Structural3000
    @Civil.Structural3000 5 ปีที่แล้ว

    This was absolutely wonderful and helpful. Many thanks for sharing this video.

  • @leonardocai7394
    @leonardocai7394 7 ปีที่แล้ว +1

    thanks for improving of engineering knowledge

  • @RuneScapeQuestMaster
    @RuneScapeQuestMaster 4 ปีที่แล้ว

    I gave up on this but what i know from the past this needs more work sir

  • @benevantmathew
    @benevantmathew 6 ปีที่แล้ว +1

    Time delay is phi(phase angle) over omega n(natural frequency).

  • @dank2265
    @dank2265 3 ปีที่แล้ว +1

    I can finally afford to go to MIT

  • @pegahbh8550
    @pegahbh8550 5 ปีที่แล้ว +1

    thank you so much, you make more easier for me

  • @billskinny7639
    @billskinny7639 5 ปีที่แล้ว +7

    “This is just the basic intro to 2004”
    Omfg.

  • @horstselzer8867
    @horstselzer8867 8 ปีที่แล้ว +2

    this is very good and super course of Basics Vibration.top prof.

  • @HughJorgan1
    @HughJorgan1 4 ปีที่แล้ว +3

    I always imagine young Sheldon sitting in the front row for these lectures.

    • @clairespeight4143
      @clairespeight4143 4 ปีที่แล้ว +2

      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

    • @bmphil3400
      @bmphil3400 4 ปีที่แล้ว

      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.

  • @ebiros2
    @ebiros2 6 ปีที่แล้ว +2

    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?

  • @johnstfleur3987
    @johnstfleur3987 2 ปีที่แล้ว

    TEACHERS ALL PAID NOW.

  • @gabrielbrasil7989
    @gabrielbrasil7989 5 ปีที่แล้ว +1

    Great explanation. thanks, from brazil!!!

  • @jackdeago3639
    @jackdeago3639 3 ปีที่แล้ว

    Lectures about Lagrangian &Hamilton mechanics

  • @malcolmanderson1279
    @malcolmanderson1279 6 ปีที่แล้ว +2

    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

  • @bobtannous6541
    @bobtannous6541 7 ปีที่แล้ว

    wonderful presentation

  • @benisdumb
    @benisdumb 11 ปีที่แล้ว +28

    he also teaches a class on comb overs.

  • @johnstfleur3987
    @johnstfleur3987 2 ปีที่แล้ว

    MY INTELLIGENCE IS ABSOLUTE..

  • @StevenTang-h8t
    @StevenTang-h8t ปีที่แล้ว

    It is good lesson for me.

  • @JJ721999
    @JJ721999 5 ปีที่แล้ว +7

    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.

    • @tumdeax
      @tumdeax 5 ปีที่แล้ว +1

      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."

    • @y.z.6517
      @y.z.6517 5 ปีที่แล้ว

      They are all free anyway. You just need to borrow text books which explain in more detail from libraries.

    • @y.z.6517
      @y.z.6517 5 ปีที่แล้ว

      It's the informatic age. Knowledge is no longer power. It's your brain and time that are valueable.

    • @7177YT
      @7177YT 5 ปีที่แล้ว

      you pay for the certificate not the stuff ypu learn.

    • @अण्वायुवरीवर्त
      @अण्वायुवरीवर्त 4 ปีที่แล้ว

      @@tumdeax Yup that's the movie

  • @johnstfleur3987
    @johnstfleur3987 2 ปีที่แล้ว

    HEAVEN.

  • @engineeringtrainingideas2334
    @engineeringtrainingideas2334 4 ปีที่แล้ว

    EXCELLENT TOPIC WHAT IS RECOMENDED VIBRATION LEVEL FOR A PUMPS ,

  • @emely8656
    @emely8656 4 ปีที่แล้ว +10

    Me in middle school being confused af while watching this; 👁👄👁

    • @cult4037
      @cult4037 3 ปีที่แล้ว +1

      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

    • @Punicia
      @Punicia 3 ปีที่แล้ว +2

      @@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.

    • @judeugwu4987
      @judeugwu4987 2 ปีที่แล้ว

      @@Punicia honestly really good advice

  • @Luiferhoyos
    @Luiferhoyos 7 ปีที่แล้ว +19

    16:48 Why are they equal?

    • @Romulo_Cunha
      @Romulo_Cunha 6 ปีที่แล้ว +8

      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)

    • @jorgesolorio620
      @jorgesolorio620 6 ปีที่แล้ว +1

      plug in ks

    • @damianblandi4294
      @damianblandi4294 6 ปีที่แล้ว

      @@Romulo_Cunha but why is it cero? I mean why do they cancel each other in that ecuation?

    • @PauliHeisenberg
      @PauliHeisenberg 5 ปีที่แล้ว +1

      ​@@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.

    • @gersongabriel3984
      @gersongabriel3984 5 ปีที่แล้ว +1

      He calculated Xs one step before, then you just substitute Xs now for the static case and you will see

  • @mohamedlaham7685
    @mohamedlaham7685 8 ปีที่แล้ว +106

    i wish study in america really ...in my university there is not even a chair to sit on it

    • @djamiladz893
      @djamiladz893 8 ปีที่แล้ว +5

      +Mohamed Laham wtf

    • @mohamedlaham7685
      @mohamedlaham7685 8 ปีที่แล้ว

      +Djamila Dz bro it is the ugly truth

    • @darkdiamond1995
      @darkdiamond1995 8 ปีที่แล้ว

      +Mohamed Laham THANK YOU:)

    • @mohamedlaham7685
      @mohamedlaham7685 8 ปีที่แล้ว

      +Ho Hoang Tu :)

    • @mohamedlaham7685
      @mohamedlaham7685 8 ปีที่แล้ว

      +Dung Le yeah man..google it by writing Fet university in jordan :)

  • @angelahall4402
    @angelahall4402 7 ปีที่แล้ว +2

    We are all created by vibration! Everything is

    • @qreeves
      @qreeves 4 ปีที่แล้ว

      I have a feeling you're not talking about string theory..

  • @Machine4977
    @Machine4977 3 ปีที่แล้ว +1

    But what does that have to do with the price of tea in china

  • @jonathanlanders9406
    @jonathanlanders9406 5 หลายเดือนก่อน

    Very helpful.

  • @RuneScapeQuestMaster
    @RuneScapeQuestMaster 4 ปีที่แล้ว

    Thank you I thought I was an idiot this makes total sense now

    • @beoptimistic5853
      @beoptimistic5853 3 ปีที่แล้ว

      th-cam.com/video/XQIbn27dOjE/w-d-xo.html 💐

  • @ankitatrey9087
    @ankitatrey9087 7 ปีที่แล้ว +86

    Want to get one of those empty seats...😍😍😘

    • @xenxkisu
      @xenxkisu 5 ปีที่แล้ว +3

      God Bless You and all the very best. Jesus Loves you and he will help you .

    • @myrongibson6314
      @myrongibson6314 5 ปีที่แล้ว +6

      only if I could pay for it.

    • @kingplunger1
      @kingplunger1 5 ปีที่แล้ว

      @@xenxkisu oO

    • @lazybean4365
      @lazybean4365 5 ปีที่แล้ว +4

      @@xenxkisu jesus are u fucked up in your brain what help

  • @SY-hf9dj
    @SY-hf9dj 4 ปีที่แล้ว

    Why am I watching this late in the night?

  • @AvivMakesRobots
    @AvivMakesRobots 5 ปีที่แล้ว

    Really great content. Thanks!

  • @hamadaguemar6006
    @hamadaguemar6006 10 ปีที่แล้ว

    merci monsieur pour ces cours

  • @chengzeng4978
    @chengzeng4978 11 ปีที่แล้ว +1

    great reminiscent

  • @kabandajamir9844
    @kabandajamir9844 ปีที่แล้ว

    So nice thanks sir

  • @foadsf
    @foadsf 4 ปีที่แล้ว

    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?

  • @المهندسةتقوى
    @المهندسةتقوى 5 ปีที่แล้ว

    رَبّيَ يَوَفَقً الُجْمٌيَْع

  • @victorkkariuki
    @victorkkariuki 6 ปีที่แล้ว

    Great lecture

  • @jackdeago3639
    @jackdeago3639 3 ปีที่แล้ว

    Thank you so so so much

  • @pallavipallavi8560
    @pallavipallavi8560 4 ปีที่แล้ว +1

    thank u sar

  • @mdaftabuddin3130
    @mdaftabuddin3130 7 ปีที่แล้ว

    Thank you sir for your lecture

  • @NisseOhlsen
    @NisseOhlsen 5 ปีที่แล้ว

    Thank you very much for providng us with such a great lecture.

  • @siviwemrausi9758
    @siviwemrausi9758 8 ปีที่แล้ว

    great video

  • @Jasonnewlook
    @Jasonnewlook ปีที่แล้ว

    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

  • @itsthesame
    @itsthesame 3 ปีที่แล้ว +3

    I really hate powerpoint

  • @ShabbirHussainy
    @ShabbirHussainy 10 ปีที่แล้ว +1

    just awesome..

  • @zagrevyum08
    @zagrevyum08 4 ปีที่แล้ว

    Excelente clase !!!! saludos

  • @RuneScapeQuestMaster
    @RuneScapeQuestMaster 4 ปีที่แล้ว

    People piss me off but hey ill catch you out side all day

  • @waronsisuA4
    @waronsisuA4 9 ปีที่แล้ว +11

    東大と問題はどっちの方が難しいのかな

  • @test2test241
    @test2test241 8 ปีที่แล้ว

    For some reason my original test message did not go through, so I'm sending a longer one, in the hopes that this one does Perhaps the first one was just too short.

    • @qreeves
      @qreeves 4 ปีที่แล้ว

      Test received, awaiting further instructions.

  • @ahmedalgarray8333
    @ahmedalgarray8333 9 ปีที่แล้ว

    nice job. Thanks

  • @patricknday833
    @patricknday833 6 ปีที่แล้ว

    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

  • @avinashdesai0206
    @avinashdesai0206 3 หลายเดือนก่อน

    Shift the angle
    respond (1)

  • @cisuris
    @cisuris 7 ปีที่แล้ว

    You are amazing, thank you

    • @qreeves
      @qreeves 4 ปีที่แล้ว

      Thanks, I try

  • @deca321
    @deca321 11 ปีที่แล้ว +1

    MIT - should go there :(

  • @RuneScapeQuestMaster
    @RuneScapeQuestMaster 4 ปีที่แล้ว

    Let's test the tension

  • @sahilrajeshgajbhiye4968
    @sahilrajeshgajbhiye4968 4 ปีที่แล้ว

    ty very much sir