How a Giant Pendulum Made Taipei101 Possible!

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  • เผยแพร่เมื่อ 25 ก.พ. 2022
  • This video explains the clever design solution that engineers employ in the design of high-rise buildings. Usually, high-rise structures resist lateral loads via steel frames, shear cores, or braced steel beams. Sometimes, these systems are not enough and engineers have to resort to other options. The video starts with a generic description of the forces experienced by a skyscraper with the main focus cast on wind loads. Furthermore, the video discusses the aerodynamic features of a building and tricks that reduce the applied wind loads. Lastly, the video explains the use of a tuned mass damper that damps out particular frequencies of the building resulting in a decreased sway of the building.
    References:
    [1] ACI SP-97, "Analysis and Design of High-Rise Concrete Buildings," USA, 1989.
    [2] D. Bennett, Skyscrapers: Form & Function, New York: Simon & Schuster Ltd., 1995.
    [3] M. H. Günel and H. E. Ilgin, Tall Buildings Structural Systems and Aerodynamic Form, New York: Taylor & Francis Group, 2014.
    [4] H. T. Breukelman, J. Robinson and J. Kottelenberg, "Tuned mass dampers under excessive structural excitation," Motioneer-ing Inc., Guelph, Ontario, 2003.
    [5] N. Eddy, "Popular Mechanics," 19 July 2005. [Online]. Available: www.popularmechanics.com/tech.... [Accessed February 2022].
  • วิทยาศาสตร์และเทคโนโลยี

ความคิดเห็น • 120

  • @user-fm2bk5oc5y
    @user-fm2bk5oc5y 2 หลายเดือนก่อน +42

    I’m a union Carpenter and have worked on many high rise buildings and I’m fascinated by the tuned mass damper, and would have really enjoyed being at the top when the earthquake happened. The video was easy to understand and the illustrations were helpful to visualize the engineering principles involved. I’m looking forward to seeing more of the videos you produce. Thank you !

    • @robertreynolds1044
      @robertreynolds1044 2 หลายเดือนก่อน +1

      My name is Bicycle Bob and I approved this message and I'm a 30 year retired Teamster.

    • @imaginova88
      @imaginova88 หลายเดือนก่อน +2

      I also approve this message.

    • @KainsAddiction
      @KainsAddiction หลายเดือนก่อน

      Fuck unions

    • @KainsAddiction
      @KainsAddiction หลายเดือนก่อน

      F u c k unions

  • @MynameisLuk4
    @MynameisLuk4 หลายเดือนก่อน +19

    Im here because I saw a video of the damper in action a few weeks ago (Taiwan earthquake). And when I saw it I immediately thought how heavy it must be and how they got it up there. But in my amateur mind I imagined that it is a hollow ball which then they filled up with lead or something similar. Really fascinating.stuff.

    • @tomarmadiyer2698
      @tomarmadiyer2698 หลายเดือนก่อน +2

      That's actually clever. Pouring molten would be an efficient way of shifting the mass

    • @AName-pp8di
      @AName-pp8di หลายเดือนก่อน +1

      It looks like it’s made of slices of steel, I think they probably craned each slice up, and stacked them on top of each other then made the bolted connections in situ.

    • @ReversePatchwork
      @ReversePatchwork หลายเดือนก่อน

      I am here because of the Taiwan earthquake and because I played a video game called Mirrors Edge Catalyst and in a mission one fell and tore through a building!

  • @JohnSmith-kf1fc
    @JohnSmith-kf1fc 2 ปีที่แล้ว +26

    Im a retired carpenter and this content was very easily understandable for me. Ive always loved science but i get lost if videos are orientated towards high level academics like videos of conferences on very specific science topics. Your videos could be twice as long and complicated and id still be able to follow.
    That being said, great video you earn my sub and full bell notifications :)

    • @TheEngineeringHub
      @TheEngineeringHub  2 ปีที่แล้ว +5

      Hi John, thank you so much for the great feedback. It makes us really happy to hear that our content is easy to follow and to understand for people of all backgrounds. We aim at explaining engineering concepts with mostly intuitive and intrinsic knowledge through simple illustrations rather than complex equations, though we do end up putting an equation or two on the screen occasionally.

  • @fahimahmedbhuiyan2252
    @fahimahmedbhuiyan2252 4 หลายเดือนก่อน +6

    I have no idea how to thank you guys...this explanation is just a gem for civil/structural engineers.❤

    • @TheEngineeringHub
      @TheEngineeringHub  4 หลายเดือนก่อน +1

      Thanks Fahim, comments like this mean the world 🙏

  • @poppy5515
    @poppy5515 2 หลายเดือนก่อน +4

    Great explanations! Thank you. Technical enough to be not simplistic or dumbed down. Good graphic to accompany the technical part. Two thumbs up!

  • @colvinator1611
    @colvinator1611 ปีที่แล้ว +2

    Very interesting indeed !
    Thanks a lot. I can appreciate the technical challenges presented to the structural designers.

  • @ansible9340
    @ansible9340 2 ปีที่แล้ว +31

    Great video, btw don't shy away from things getting too complicated.

  • @forkliftofzen5318
    @forkliftofzen5318 2 หลายเดือนก่อน +3

    I live where ground-level straight-line wind speeds well in excess of 100 KPH are common and we never have rail cars of any kind blow over.

    • @TheCerovec
      @TheCerovec หลายเดือนก่อน +1

      Exactly. In my country,in the coastal regions we have 100km/h wind gusts. And we also don't have train carts flipping over.

  • @raydunakin
    @raydunakin หลายเดือนก่อน

    Very interesting and well done!

  • @jovenjuli
    @jovenjuli ปีที่แล้ว

    Your simplified explanation is on point, keep it up.😊

  • @gary9793
    @gary9793 2 ปีที่แล้ว +3

    As an engineering student i definitely find this channel more than interesting. Thanks for the content!!

  • @ravshanbekmavlonov2996
    @ravshanbekmavlonov2996 ปีที่แล้ว

    Great video! The whole world using your content to get new knowledge.

  • @stevelawrie7087
    @stevelawrie7087 หลายเดือนก่อน +1

    Good video, thanks, very understandable

  • @JoseJimenez-we3te
    @JoseJimenez-we3te 2 หลายเดือนก่อน

    Excellent, concise and clear video. I look forward to exploring more of your videos.

    • @TheEngineeringHub
      @TheEngineeringHub  2 หลายเดือนก่อน

      Awesome, thank you very much Jose!

  • @NZdazza
    @NZdazza 2 หลายเดือนก่อน +1

    Well done, that was relatively easy for this non tech guy to understand

  • @lindsay_1849
    @lindsay_1849 2 ปีที่แล้ว +2

    Such a great video David!

  • @flourishomotola5306
    @flourishomotola5306 2 ปีที่แล้ว

    High quality video. Thanks a lot bro 🙏🏿

  • @hlbrbck2273
    @hlbrbck2273 2 หลายเดือนก่อน +1

    I wanted to know and this video was simple enough and technical enough for me to grasp and understand. I also appreciate your ending comments regarding other factors/forces that must be considered. I am not a science/engineer minded person but have a great respect and interest. This video allows me to learn AND understand enough!!

    • @TheEngineeringHub
      @TheEngineeringHub  2 หลายเดือนก่อน

      I love reading comments like this; it's so rewarding! Thank you for stopping by and also for taking the time to write this. Cheers!

  • @cheeseisdelicious111
    @cheeseisdelicious111 ปีที่แล้ว

    Excellent video, completely understandable and thoroughly fascinating.

  • @SJR_Media_Group
    @SJR_Media_Group ปีที่แล้ว +4

    Great video... your presentation of complex concepts were delivered in everyday terminology. There was enough information detail to keep engineering geeks like me attentive. I can recall several structures classes in college. We discussed building sway and it's effects on buildings. The primary concern is structural, building has to stand, not collapse. The second concern is motion that might cause a building occupant to literally get sea sick.
    I have been in a number of high rises. On several occasions wind did make building sway. The motion was very slow and barely noticeable to the average person. I knew it was swaying because I sighted edge of window frame on a distant object. It appeared as if the distant object was moving, but the object I stood in (high rise) was actually moving.
    The poor guys who really have it bad on a windy day are the window washers. I think I'll pass. I'm not afraid of falling from extreme heights, I'm afraid of extreme stopping when I hit the ground.

  • @dwaynemurphy8229
    @dwaynemurphy8229 ปีที่แล้ว

    Great video! Well explained.

  • @maryguthrie258
    @maryguthrie258 2 หลายเดือนก่อน

    Wonderfully explained, easy to understand. Thanks so much for this information.

    • @TheEngineeringHub
      @TheEngineeringHub  2 หลายเดือนก่อน

      Thank you Mary for tuning in 🙏. Regards!

  • @dhlong1697
    @dhlong1697 หลายเดือนก่อน

    Every time I visit Taipei, I revisit Taipei 101--just to gaze at the pendulum.

  • @victorcarubelli
    @victorcarubelli 2 หลายเดือนก่อน

    Great video! Simple and objective, thank you

  • @Mike-vr4lw
    @Mike-vr4lw หลายเดือนก่อน

    Great video, educational, fun, and understandable. Thanks, I've subscribed 😀

  • @gerardomoonshine4984
    @gerardomoonshine4984 หลายเดือนก่อน

    Fine explanation. Thanks

  • @user-xw9fd1ku6x
    @user-xw9fd1ku6x 2 หลายเดือนก่อน

    Thanks for sharing. I am not connected with engineering but found this most interesting 😊.

  • @engrfawadiqbalkhan786
    @engrfawadiqbalkhan786 5 หลายเดือนก่อน

    I appreciate your efforts ,brief and concise video .Thankyou for sharing , Tall structures are more vulnerable to wind loads because the frequency of wind loads and tall structures is lower there is high probability of frequencies' matching and resonance will occur if frequencies are matched and as a result violet shaking of the building will occur .

  • @joeblough4605
    @joeblough4605 หลายเดือนก่อน

    Good video, thanks.

  • @duderino1950
    @duderino1950 ปีที่แล้ว +1

    I’ve just discovered your excellent channel and subscribed immediately. The people who will be interested in watching your explanations will also have some grasp of at least basic physics and math so I 8:23 think you could easily delve into a bit of this. You could even have a few lectures covering basic concepts of structural engineering and materials. I’d love to see them. A good educator does not talk down to the level of his audience, he or she stretches their understanding up. It’s called learning.

    • @TheEngineeringHub
      @TheEngineeringHub  ปีที่แล้ว

      Thanks for the feedback, duderino. I hope you didn't feel that I talked down to the audience. I just wanted to ensure that everyone is still on board and get a feel for what the audience appreciates and wants more of. Cheers!

  • @hg2.
    @hg2. หลายเดือนก่อน

    Good introduction.
    Now I'd like to see a level 2 of this material, focusing on earthquakes.
    There is a video of the Taipai Tower during the latest earthquake.
    I sort of "get" how the damper works, but I want to see it second-by-second, with a contrast of what would happen if the damper weren't there.

  • @stevemyers2092
    @stevemyers2092 2 ปีที่แล้ว +1

    All of it. I live in Vancouver BC - we have a building here that has a center core and the "building is hanging from that internal tower by cables and rubber" it works.

  • @TheBuildingExpert
    @TheBuildingExpert 2 ปีที่แล้ว

    great video 👍

  • @alideep9656
    @alideep9656 ปีที่แล้ว

    All of it, it's full of useful information, thank you ✌🏻✌🏻

    • @TheEngineeringHub
      @TheEngineeringHub  ปีที่แล้ว

      Thanks Ali, we are glad you enjoyed it! Makes it worth the time!

  • @Isidore_Chitosi
    @Isidore_Chitosi 2 ปีที่แล้ว

    amazing innovation🙌

  • @JaymesEaston
    @JaymesEaston ปีที่แล้ว

    Outstanding!

  • @catherinevankampen1262
    @catherinevankampen1262 3 หลายเดือนก่อน

    My kids & I just watched! We learned a lot. Probably 30% was too difficult, but I am ok with that as I mostly focus on History so my science knowledge needs work! We subscribed!
    Also, I was up in Tapei 101 in the fall of 2004 and got to see the ball....so cool.

    • @TheEngineeringHub
      @TheEngineeringHub  3 หลายเดือนก่อน

      That's great! Thanks for taking the time to write this feedback. I really enjoy when viewers express their opinions. The mass-tuned damper concept is extremely interesting and has many applications. If your kids found it cool; it may be good to consider a career in engineering ☺ When I was a teenager I was always fascinated by technologies like this. It led me to the engineering field. Never regretted that decision. Cheers and thanks for the subscription!

  • @kafka9627
    @kafka9627 2 ปีที่แล้ว +2

    Im a non engineer interested in engineering and this video was the perfect mix of details and not details. I loved when you said that xyz are simplifications - it sparked more curiousity while making me able to understand instead of getting bogged down in details - BUT, and this is critical, I also didn’t have to get stuck on not understanding how or why that thing is

    • @TheEngineeringHub
      @TheEngineeringHub  2 ปีที่แล้ว +1

      Thank you so much Alice, comments like this is what gives us the motivation to produce more content. We are so happy you liked our video. Regards!

  • @pieteri.duplessis
    @pieteri.duplessis 2 ปีที่แล้ว

    Well done.

  • @davidgriffiths7696
    @davidgriffiths7696 2 หลายเดือนก่อน +1

    It was easy to understand. Mechanics is simple. Cross wind displacements and torsional displacements should be added, as the other stuff about resonance, height, stiffness etc is well known and self evident.
    I invented a new structural innovation to my self build house with a 2 metre cantilever: prestressed steel springs that ingeniously pivots the entire weight of the overhang section back to the centre of the structure as an equal and opposite moment. This prevents strain deformation of the timbers over time, as the springs react with the same force as the weight of the over hang. The half ton over hang is thus supported by embodied field repulsion in the bent springs.
    Good video, clear, concise…engineers should govern nations instead of criminals.

    • @TheEngineeringHub
      @TheEngineeringHub  2 หลายเดือนก่อน

      Thank you sir! You are absolutely right, vortex-induced-vibration and torsional loads are often much more difficult to deal with but less known to the average viewer. Also your beam element sounds very interesting! Cheers and thanks for stopping by!

    • @davidgriffiths7696
      @davidgriffiths7696 2 หลายเดือนก่อน

      @@TheEngineeringHub maybe…perhaps you could include some fluid dynamics, periodic vortical regimes, chaotic regimes v wind velocity, resulting asymmetric pressure differentials leading to twisting forces on steel frames opposed for example by our good friend the triangle brace.

  • @smitrotti
    @smitrotti หลายเดือนก่อน

    Very interesting.

  • @ajazmahemoodsayyed4122
    @ajazmahemoodsayyed4122 2 ปีที่แล้ว

    Amazing sir

  • @neelamrani-vy3yz
    @neelamrani-vy3yz ปีที่แล้ว

    Very nice

  • @prodiptobhakta6587
    @prodiptobhakta6587 ปีที่แล้ว

    thanks

  • @academiceducation9780
    @academiceducation9780 ปีที่แล้ว

    Thank you

  • @hafeeznoormohamed1259
    @hafeeznoormohamed1259 2 ปีที่แล้ว +4

    very well done!

  • @omniyambot9876
    @omniyambot9876 2 ปีที่แล้ว +2

    wait what? I'm watching a video with less than 10k views? Excellent excellent job. Please make it more technical, I'm assuming people are more curious to know more!
    I'm confused with this mass damper thing for a long time since I was a child because I thought it will only transfer the kinetic energy to the "mass damper" and still, what's the point? they will reach an equibillibrium then the overall energy of the sway is still the same. Thanks for reminding me what the "damper" means lol. Apparently, it dissipates heat, which makes absolute sense. Gonna binge watch your videos bro. Sorry for bad English.

    • @TheEngineeringHub
      @TheEngineeringHub  2 ปีที่แล้ว +1

      Thank you so much Omni, we are so glad you found the video interesting. We will keep doing what we are doing and hopefully more people will start enjoying our channel in the future.

    • @brucelomax3375
      @brucelomax3375 2 ปีที่แล้ว +1

      I speak only English and your is better than anything else could I could speak.

    • @omniyambot9876
      @omniyambot9876 2 ปีที่แล้ว

      @@brucelomax3375 I've just learned 80% watching youtube and reading comments and also commenting. Thanks man.

    • @TrggrWarning
      @TrggrWarning 2 ปีที่แล้ว

      @@TheEngineeringHub awesome!! this gets us closer to the answer i asked in other vid. Thank you

  • @chanmakaravat9398
    @chanmakaravat9398 ปีที่แล้ว

    Amazing video, what software you are using (at 7:17) to model the structures with and without tune mass damper. I should try modeling myself and see. Thank you bro

    • @TheEngineeringHub
      @TheEngineeringHub  ปีที่แล้ว +1

      Thanks Chanmakara, the software is called Algodoo and is free. It is a good physics engine for modeling all sorts of physics. See link: www.algoryx.se/algodoo/#:~:text=Algodoo%20is%20FREE%20for%20Windows,scenes%20that%20have%20been%20shared.

    • @chanmakaravat9398
      @chanmakaravat9398 ปีที่แล้ว

      Appreciate it.

  • @ezegroup22
    @ezegroup22 ปีที่แล้ว

    I understand!

  • @steelramesh
    @steelramesh 2 ปีที่แล้ว

    nice one

  • @Myrslokstok
    @Myrslokstok หลายเดือนก่อน

    I think it is not only the wind pushing, it is also the sucking on the other side!

  • @busybeenature9092
    @busybeenature9092 6 วันที่ผ่านมา

    Great. Could understand that the pendulum is set in such a way that it helps the building to survive if the wind is blowing towards it. Am I right? Thanks

    • @TheEngineeringHub
      @TheEngineeringHub  6 วันที่ผ่านมา

      That's right! It's tuned in a way to counter act the oscillation of the building

  • @jarvisa12345
    @jarvisa12345 2 หลายเดือนก่อน +1

    A video showing the Taipei 101 damper swaying during an earthquake:
    th-cam.com/video/Tkz6b7Q3dRk/w-d-xo.html

  • @marcse7en
    @marcse7en 2 หลายเดือนก่อน

    Surely swaying of tall buildings will cause damage to the fabric of the building, especially cumulative damage over time? For example, stress cracks, metal fatigue, and the like? I'm assuming that routine checks will monitor for this?
    Q: A question is "weighing" on my mind! ... What happens to the people and floors underneath the 730 ton Taipei ball, should it fall? ... Nothing good, I'll wager? ... The engineers will be in "bits?" They'll be "crushed?"

  • @mist273
    @mist273 หลายเดือนก่อน +1

    5:20 Eiffel Tower: 😎

  • @spiralminus
    @spiralminus หลายเดือนก่อน

    As a baker when I watch engineering videos it makes me wish I stayed in school.

  • @simon1italy
    @simon1italy หลายเดือนก่อน

    I can see how a counterweight like that could help during an earthquake, but what happens when the wind blows in one direction for a sustained period of time? The building should start swaying but then stay into that position, the weight of a sphere like that would be moved in a not advantageous position within seconds. The way I understand this is that it can only help with sudden movements, not with sustained leaning into any direction. Did I miss something?

    • @TheEngineeringHub
      @TheEngineeringHub  หลายเดือนก่อน

      Yes, there is something to that. What the video doesn't mention is that the MTD only damps out the worst frequencies (resonance) but it slightly worsen the frequencies around it. See this plot for example: www.spiedigitallibrary.org/ContentImages/Proceedings/10166/101660C/FigureImages/00022_PSISDG10166_101660C_page_5_1.jpg
      To your point about winds sustained for long periods, this case is not too critical as it will be very far from the resonance range so the MTD won't really be activated, the structure can handle that alone. The MTD is only activated when the blowing of the wind is synchronized with the swaying of the building (i.e. resonance) that is where the danger lies.

  • @neelamrani-vy3yz
    @neelamrani-vy3yz ปีที่แล้ว

    Please make video on power spectrum of wind

  • @ironteacup2569
    @ironteacup2569 ปีที่แล้ว

    Go into all the details please

  • @HDXFH
    @HDXFH 2 หลายเดือนก่อน

    5:00 weght lol

  • @caangngungkulanpoek1604
    @caangngungkulanpoek1604 2 หลายเดือนก่อน

    👍👍

  • @ReversePatchwork
    @ReversePatchwork หลายเดือนก่อน

    I am here because of the Taiwan earthquake and because I played a video game called Mirrors Edge Catalyst and in a mission one fell and tore through a building!

  • @sterlingwallstrum8975
    @sterlingwallstrum8975 ปีที่แล้ว

    What software is shown @7:17?

    • @TheEngineeringHub
      @TheEngineeringHub  ปีที่แล้ว

      It's a free physics engine called Algodoo.
      www.algodoo.com/

    • @sterlingwallstrum8975
      @sterlingwallstrum8975 ปีที่แล้ว

      @@TheEngineeringHub Very Cool! What a great learning tool! And is that device at the bottom reading groundmovements or inducing them?

    • @TheEngineeringHub
      @TheEngineeringHub  ปีที่แล้ว

      Yes absolutely, it's a very interesting tool to play with! That device at the bottom is recording/monitoring the oscillations at the top of the model. The induced displacement here is from a wind force distributed along the building's height.

  • @Hexagon234
    @Hexagon234 2 ปีที่แล้ว

    WOW I NEVER NOTICED TAIWAN NOW HAS 3D I WAS WAITING FOR SO MANY YEARS FOR TAIPER 101 TO GET A 3D IN GOOGLE EARTH

    • @TheEngineeringHub
      @TheEngineeringHub  2 ปีที่แล้ว

      hah! we are glad that is available for you now

    • @Hexagon234
      @Hexagon234 2 ปีที่แล้ว

      @@TheEngineeringHub yeah I never noticed that Taipei has a 3D I was waiting for so many years

  • @Rafal_Stajniak
    @Rafal_Stajniak ปีที่แล้ว

    limit, hmm, this is only for concrete buildings, because they are weak and brittle, while metal is flexible, and now you can build a twelve-kilometer tall skyscraper vertically, :)

    • @TheEngineeringHub
      @TheEngineeringHub  ปีที่แล้ว

      Hi Rafal, for sure steel is more ductile than concrete but when it comes to flexibility of skyscrapers the height is by far the most important parameter. It appears cubed in the formula so it affects the behavior in a nonlinear manner. The flexibility of tall structures is great for earthquakes but does not do well with typhoons. The resonance frequency of the wind gusts is low enough (high period of vibration) to match the vibrations of a skyscraper and then problems occur. Anything above 500m tall requires a careful aerodynamic analysis.

    • @Rafal_Stajniak
      @Rafal_Stajniak ปีที่แล้ว

      @@TheEngineeringHub Hello - according to my calculations, the height of a steel or metal skyscraper must be proportional horizontally to ensure its stability, it is not profitable to build skyscrapers on a small area and spend enormous money on the quality of materials, the currently known method of building skyscrapers on a small area is not profitable because such structures are just covered by the height limit, one particular skyscraper will be enough than ten small ones, and this action reduces the cost of maintaining the building

    • @Rafal_Stajniak
      @Rafal_Stajniak ปีที่แล้ว

      @@TheEngineeringHub hello - I designed my skyscraper which at the base, one of the sides of the wall, is 1000 m, and is 4000 m high, the top roof is 70 m, looks almost like a pyramid, and is stable, it is only a design, real, to be done, the cost of construction exceeds the cost of high-rise buildings at present

  • @EricPham-gr8pg
    @EricPham-gr8pg 2 หลายเดือนก่อน

    It can fall down

  • @randyfitz8310
    @randyfitz8310 หลายเดือนก่อน

    You don’t need to “dumb it down” this much.

  • @MrMockingbird1313
    @MrMockingbird1313 ปีที่แล้ว

    Most of the video was understandable. But, I had trouble with the names of the places. Consider adding a few subtitles.

  • @Zorlof
    @Zorlof หลายเดือนก่อน

    Having bought an engineered building and seeing it fail during an ice storm, I have zero confidence in Engineers. You would not catch me in a structure that involved the "engineering" principles of late.

  • @pradap2298
    @pradap2298 2 ปีที่แล้ว

    savants

  • @kytddjj
    @kytddjj 2 ปีที่แล้ว

    .

    • @pluto9000
      @pluto9000 2 หลายเดือนก่อน

      ..

  • @peternicholsonu6090
    @peternicholsonu6090 ปีที่แล้ว

    Sway too much for me.

  • @janl8916
    @janl8916 หลายเดือนก่อน

    What I find difficult to understand is, that someone with a decent enough command of English to narrate a video could be oblivious to the pronunciation of the "ch" sound in words like technology or technical. How could you go through life, learning all the engineering jargon and yet look past something as simple as the pronunciation of a pair of letters

    • @TheEngineeringHub
      @TheEngineeringHub  หลายเดือนก่อน

      I could have definitely done better here. It sounds like this video needed a few more narrations before getting to the final version. But if that's the main mispronunciation that you picked up than I am actually happy. Obviously English is not my first language so I mispronounce words often. Especially when I am focusing on something technical, as if the language part of my brain just turns off so that the mathematical part can get a bit more compute.

  • @HRubeus
    @HRubeus 2 หลายเดือนก่อน

    Nobody says that the project of the pendulum was made by Ing. Renato Vitaliani of Padua, Italy!