Understanding Vibration and Resonance

Watch the companion video on pendulums here: nebula.tv/videos/the-efficien...
In this video we take a look at how vibrating systems can be modelled, starting with the lumped parameter approach and single degree of freedom models. We then go on to look at damping, the dissipation of energy that occurs in all real systems, as well as forced vibration, resonance and multiple degree of freedom models.
---
ERRATA:
- At 04:16, the terms sqrt(k/m) appears not in the equation of motion, but in the solution to the equation of motion
---
For further reading I'd recommend the following:
- J. L. Humar - Dynamics of Structures
---
The Efficient Engineer is a channel aimed at mechanical and civil engineers. The mission is to simplify engineering concepts, one video at a time!Follow me on Twitter: / efficiengineer
---
If you would like to support the channel, please consider becoming a Patron - / efficientengineer . This will allow me to create more high quality videos covering a range of engineering topics.

[@TheEfficientEngineer]

This was my first video on dynamics, so I hope you enjoyed it! Let me know which topics you'd like me to cover next. Don't forget you can watch the companion video on the oscillation of pendulums on Nebula - nebula.tv/videos/the-efficient-engineer-the-oscillation-of-pendulums

[@CanadianIndian88]

Please consider a doing a video on Heat transfer and thermodynamics. I can provide you with many more real world applications and topics as well. Thanks.

[@christopherevans195]

I agree with @@CanadianIndian88 Heat transfer and thermodynamics would be great. @The Efficient Engineer Although finishing the materials series (polymers, ceramics, and composites) would be very nice. Thank you for all your hard work on these videos. I am always excited to see you post a new video. Creators like you among others are convincing me to sign up for Nebula and Curiosity Stream.

[@TheEfficientEngineer]

Heat transfer is probably going to be next. Hoping to cover thermo at some point too, just not sure where to start!

[@CanadianIndian88]

@@TheEfficientEngineer awesome! Keep up the great work man!

[@NILESHGCEK]

Please make a video on acoustic emissions use in pressure tests of tanks covering sensors, preamps theory with animation

[@MatanF15]

The impact you have on future/beginner engineers is the same as when the forcing and natural frequencies match. You are truly a hero, each of your videos sums a whole semester of useless old boring lectures.

[@hamzamohamed7935]

I like how you match his efforts with the natural frequency 🫡

[@Freshboyarly]

This man's channel needs a lot more viewers. His work is exceptional. Thanks much for always giving us quality content.

[@KAALBHAIRAV.]

Absolutely right bro

[@ramsundarsankaran3319]

Agreed

[@ethanlawrence2825]

Damn right, this video is absolutely excellent !! :)

[@kgakgamatsotsagae8437]

I concur

[@mfahim517]

Ikr? Why is this channel not famous? I love every single one of his videos

[@priyansutank]

Oh man, really?! I just finished the whole vibration Dynamics in last sem and this video explains all that stuff. One thing I wanna say, the topics you choose are directly connected to the academic syllabus. ◽Keep going!!!

[@PetraKann]

Recapitulates?

[@priyansutank]

@@PetraKann hey I just wanted to type anything because I was eagerly waiting to see the video that's why!

[@roshanantony7467]

@@priyansutank understandable! The excitement when we finally understand a difficult concept is a totally different feeling! Cheers!

[@kuuno2]

Same here xP and I can agree on academic point!

[@first9_yt]

@@roshanantony7467 yeah...

[@alexevans4741]

I've already finished my degree in engineering and I still find these videos helpful and amazing, can't believe he summed up in 5 mins what took me weeks to learn. Great work can't wait to watch the next video

[@mathijspiessens8318]

Its absolutely CRAZY how good these videos are, a general university needs HOURS of lectures with static powerpoints to explain something which can be explained like this so efficiently. Its absolutely mindblowing, sadly these videos release a few months after i passed the exam. But that doesn't stop me from enjoying these videos! Thank you sir!

[@yashwanthm5011]

The best explanation videos on youtube exist on this channel. I truly believe the community you have here is more than happy to watch an hour-long in-depth video series! It would be definitely the best.

[@maramalkhlaifat8673]

I can’t express enough how glad am I that I have found this channel, it explains the concepts in such a wonderful way, THANK YOU! Keep going!

[@yoniakselrud2291]

I literally started this course today shared the video with my fellow students and just amazed at the simplicity,visuals, and great content always a treat to get a new video keep up the good work!!

[@med7756]

You really need to be certified for your great efforts. Without this video, I would've never understood what is going on when a body vibrates! Thanks from my heart, you're a hero!

[@adamhaly4263]

Truly incredible work. Took statics and dynamics 3 years ago and need it for a class now. This was a great refresher

[@nanodynamics5203]

Wow. You summarize the whole semester course in 20 min and you made vibration concepts crisp clear. I would definitely recommend your channel to all engineers.

[@med7756]

That's why his channel includes the term ''effecient''.

[@Emptiness-]

This is a whole semester worth of dynamical mechanics in under 20 min... Hats off to the efforts in making these visual teaching material!

[@kalemnorris3687]

Your videos have given me a better deep conceptual understanding than nearly all the lectures I've had in 4 years of Mech Eng, thanks dude

[@kristofferh2312]

This is gold, have been watching your channel throughout my 5 years of university, and next year I will be a better engineer thanks to you guys🙌🏼

[@Thekingslayer-ig5se]

You literally explained such a huge concept with such ease!! People like you can save a lot of people. Your contribution is so vital and essential for the society sir. Keep continuing!!

[@ShailendraSingh-dn3bm]

Beautifully explained and visualize Mechanical vibrations... Never thought someone explain these difficult Mathematics and Physics behind this... A VERY BIG THANKS TO YOU

[@shaishinator7233]

This is the single best video which sums up half of mechanical engineering, controls, vibrations, and more. I took so many courses for years and struggle to link them together but this video seamlessly explains the importance of all this theory I've learned. Using this whole channel to prepare for technical engineering interviews, thank you so much for this amazing work!

[@user-vi3pi9rf7w]

Just rewatched failure theories This is going to be great. Your videos are carrying future engineers single handedly.

[@willson8246]

This video clip is super super awesome. The detail is very easy to understand and the equations as well. The video animation can describe the model behavior of the system. The ones who created this video are helping to huge number of people to get knowledge. I appreciate to the the staff team. Really love this channel. Really thanks.

[@AJ-et3vf]

Awesome! I love this! I took Vibrations earlier this year and it was quite the interesting topic. I highly appreciate seeing this video about vibration and resonance especially knowing the production quality of the videos of this channel ❤️

[@naseralbadareen3527]

The Best video explaining this topic i have ever seen , the 3D visuals you add incredible amount of times to understand it , loads and loads of 2D boring graphs that are not letting anyone to actually imagine what happens correctly . Thanks !

[@cocojoy1590]

You will be blessed forever…best explanations,animations,graphics,resolution of physics videos on internet. You deserve much more subscribers than 400k!

[@grizzsimbol4441]

I wish this channel existed when I was in college but still great refresher. Thank you and keep up the great work!

[@jjohn1234]

We just covered this in the mechanics lecture this week! This video is at my current max level of understanding, really cool to see. It combines all courses in my first module. Calculus, Mechanics and Lab. Cool to see how it all comes together.

[@lingarajmishra8981]

This video was like summary of the mechanical vibration course curriculum for the under grad and post grad level.. excellent coverage , thank you for replenishing what I studied 🙏

[@benjamin.kelley]

I really liked this course when I was in school, finally applying calculus and physics to solve time-based problems. Plus it felt so good to get the 2 page long homework problems correct after 30 minutes of writing. This is about one semester and over 200 hours of my life packed in one video haha

[@blu3fish]

I am a mechanical engineer and your content so incredibly good. This is what everybody shall hear before digging into details during the lectures. Wish you all the best in your life. Thank you.

[@rodericksibelius8472]

Thank You for posting this: I was an aircraft mechanic for 8 years in the US Navy and trained, schooled, worked on Aircraft Hydraulic Flight Controls Systems, Airframes and Structures, AND LATER, I went to work at Lockheed Space Systems Division Environmental Structural Laboratories where I worked with Vibration/Acoustic tests on spacecraft structures. This video extends my knowledge and understanding of the physics from that experience.

[@albertoaravenacastro9525]

The amount of studying you have to do to make this kind of videos must be huge, thank you!!!

[@tusharkuldeep4530]

What a beautiful lecture,it conclude the whole vibration in just 20 minutes,your all videos are really really helpful.thanks

[@omaicatobi301]

Man, as a mechanical engineer who studied vibration dynamics, I really really appreciate your efforts and this fabulous explanation bout vibration

[@nadjetaklamos6945]

I shared the video with my students and just amazed at the simplicity visuals. Good work!!

[@drpyne4628]

One of the finest explanations floating all over internet. Thanks and all the best!!

[@jakephess]

omg… THANK YOU!!! i am doing a senior design project on vibration absorbers in tall buildings for my engineering degree and you literally made this just at the right pace for me.i will for sure be referring you in my paper! 😻

[@jacopobalsamini1031]

omg, you just made my day! the Mechanical Vibration is the most fascinating stuff on whole engineering field imo. ty so much for your work, your explanation are pure gold! from italy

[@user-rq5oo5zw4p]

Omg, I wish I’ve watched this video during my Mechanical System Dynamics and Vibration mechanics classes…Amazing job lads!

[@leonhill8447]

Now *this* is some real engineering, presented very efficiently when played at 1.5 speed :). Very well done!

[@sofiansaleh]

I knew all of this but the way you explained it makes me wish you uploaded this earlier, so well put together its amazing thank you

[@V-for-Vendetta01]

same lol, i had vibrations the previous semester.

[@staircasefunction9124]

You deserve a lot more subs. Please continue uploading. Your content is exceptional

[@zhenoob]

I'm ashamed to say that I had largely forgotten about this a few years after graduation.. but I stumbled upon your channel, and it's inspired me to learn again!

[@abhipatil1]

Thanks for creating this video. What a simple way to explain the concept which seems to be difficult after looking at text for hours. You saved the day 🙏

[@devinotero1798]

one of the greatest channels of all time. engineering wouldn't be the same without you

[@FrankTheTankX4]

You are a 1000X better at example fundamental than the majority university professors!!!! Keep making videos!!! Thank you!!

[@ManishKumar-wh1tz]

Thank you for your great animation videos. These help a lot in visualization while studying those thick books. And also keeps up the interest.

[@Goose____]

This is how teaching should be done, i understand much better when what i learned is taught in an intuitive way, linked to real world cases and explained well, this so much better than staring at laws written in a textbook with 0 context and a bunch of exercises, thanks alot

[@merc6380]

Dude I am a 3rd year chemistry major, and never understood why more mass means less frequency. I googled, looked at textbook which assume the reader already knows, but this video cleared that up. Huge thumbs up from. Appreciate it my bro.

[@mohammednimir1478]

Thank you for your great videos, they are really very helpful. I hope you can make more videos in this topic with more details and much complex problems. I know it takes a long time and big efforts to make such great videos, but it will be great if you can post more frequently.

[@ch.prabhanjanpatro1965]

The entire basic concept starting from a simple mass spring system to resonance in 20 mins is just awesome. Very well explained with dynamic visuals. 10/10 bro 👍

[@carlosquintana1664]

Great job!! You explained a lot of concepts in a very understandable way. Congrats

[@sach7316]

Thanks a lot for making me understand the dynamic in better way. Very nicely presented the dynamic of mass. Expecting more video from you in near future.

[@Maderum]

Man you are really doing awesome work. Thank you so much! Keep it up man and know that your work has a profound effect on young, future engineers!

[@davidjohansson7646]

When i changed my suspension in my car I basically saw this design. A spring holding the cube ( the car.) With a damper (shock absorberer) in the middle. Now i understand better how the vibration acts upon my suspension. Fascinating to se how vibration theory applies in the real world!

[@arthuriasbeck5015]

This was the best video I saw on this theme. Congratulations. I'm starting to study rotating machinery in my Phd and this video was very useful. Thank you a lot!

[@kittyblossom7342]

😳 All the basics explained in just a 20 minute short video!! And here I was studying it for a minimum of one week. Why didn't I discover this video earlier!! 🤦🏻‍♀️ You made my life so much easier.

[@serenkzsar7494]

You're a lifesaver. Keep doing it please. I feel like I've found a treasure 😌Fluid Dynamics, Aerodynamics, Numerical Methods, Plasma Physics these are the topics that I wanna see much more :)

[@mounsifcherfaoui121]

I wish I saw this video 3 years before, Well explained with a great visualization. Keep posting new videos man!

[@boowboow311]

Thank you so muchhh!!! Your video helped me understand the lessons that my lecturer taught me for 4 weeks. Please continue making this kind of video!!! Your videos are so coolll and easy to understood. I love your videos so much!! 👍👍👍

[@abdulkabeer11]

This video is such densely packed with information, I learned more in this video than my 2hr lecture in University/zoom.

[@japalocoturbo]

Oh boy can't wait to take vibration class in a few semester, surely this will help. The QUALITY!!!

[@tarymaas]

These videos are simply amazing. They should be a mandatory part of all university curricula.

[@rubal1738]

Bro what an amazing video you put a lot of work in your videos and that too for free i love it. Our college takes so much money from us but the teaching is incomparable to your videos. 🙏🙏

[@mohammedmhilal4129]

I just started my vibration class so this came at a perfect time. Thanks!!

[@eng.mustafajaber2780]

Thank you very much for your explanation. The animations are so clear to understand the dynamic response. All the best✌️

[@adithyaprakash200]

This is almost a bachelor's semester course. That too precise to the point . Thanks man, you are doing god's work.

[@nitishbarnwal3663]

Great job sir. It took 15 days to understand the theories in college. But you have cleared theory as well as visualisation too with 20 minutes.

[@ThiruT85]

I am automotive, heavy engineering, power train structural designer and analysist and every time read and see related to vibration each time looks like new thing always... explanation and video makes simple and better to understand. Thanks!

[@amritregmi5034]

Thank you brother for such a good explanation. I knew these things. But the way you explained. That is absolutely incredible.

[@qudhachure9598]

I am taking dynamics right now. I might watch this video more than one time just to be ahead of myself. Plus watching this is so satisfying beside that it’s my interest.

[@enami_0136]

Do you know any KZbin channels that explain exercices in dynamics ?

[@qudhachure9598]

@@enami_0136 Yessir Try (questions and answers) That channel is awesome Or just write dynamics in KZbin You’re gonna get variety options.

[@enami_0136]

@@qudhachure9598 thank you

[@fanman421]

Thank you for your work on this video! Excellent descriptions and graphics. I worked for just over 20 years in vibration analysis and balancing in industrial settings. Mostly balancing large rotating industrial equipment such as cooling tower fans and large blowers. I have seen the catastrophic results that unbalanced rotating equipment can cause. In one instance a large cooling blower (500 Hp motor with a 6 Ft diameter fan) was vibrating very heavily at the rotation speed of 1,725 RPM. On the side of the fan housing, the maintenance workers had written the dates of replacement of either bearings, or bearings and shaft, for several years with the time intervals being about 3 months apart. The cost of replacing couple of large pillow block bearings and the 4 inch diameter shaft every few months was tremendous. After balancing the fan rotor, that fan was in operation for at least 8 years without a single bearing replacement (when I retired). $150 balance job saved 10’s of thousands of $ in maintenance costs. In another instance, a stair handrail was shaking fairly violently not far from a vibratory conveyor system. When a person grabbed hold of the handrail, it would stop shaking due to the dampening. I told the maintenance supervisor “I can fix that shaking handrail in under a minute.” And he said “Do it.” So I took one of my balance weights (1 Lb) and a self drilling screw out of my tool bag, grabbed my impact driver and attached the weight on the handrail vertical support just below the top of the handrail. The shaking stopped !! I just altered the resonant frequency enough so it no longer shook in sympathy with the conveyor unit. 😉

[@oneliobest3181]

I have joined the performance guys under condition monitoring doing balancing and vibrations. Please can you help with some sources to help me kick start my new line of work. I look forward to do certifications as well.

[@brucelytle1144]

I did vibration analysis in the Navy. One time a motor/generator set came through the shop for final qc and passed with flying colors! They installed it on the ship and it made a godawful noise! We checked everything, looking for anything that would have tweaked it during installation, nothing. I put an accelerometer on the deck, hit the deck with a hammer. Bingo! Same frequency as 2 x the rotational speed. Right on frequency! It was a bit more complicated to change frequency of the deck, as underneath was a fuel tank... But it did fix the problem. Never found out what caused the change in natural frequency in the first place though.

[@fanman421]

@@brucelytle1144 Yep, natural resonance of surrounding structures can be notoriously difficult to identify. A large exhaust fan (125 HP) was making a horrible loud roar at speed. The sound was 6 times the RPM of the fan rotor and one steel panel of the outflow duct was vibrating like a drum head in motion in the center about 1/4”. Fan had 6 blades. 🤔 grabbed a welder and put a piece of angle iron diagonally across that one panel and tack welded it in place. Ran the fan again and near silence. 😉 Thank you for your service! 9 years USAF Avionics ground equipment myself. F15 was my bird.

[@MWang-ne9ze]

I didn’t fully understand the damping mechanism in AC circuit analysis until I watched this video in a completely different field, I feel blessed!

[@nguyenleo5925]

It's really helpful. I can understand the vibration theory within 20 minutes instead of reading more than 300 pages of document. I can use your instruction to make the design of dynamic solution more effectively. Thank a lot!

[@engrfawadiqbalkhan786]

This video just summarized all of my Structural Dynamics and Earthquake Engineering Course of Master's in Structural Engineering in less than 20 minutes ,Well done.

[@Traderhood]

Dude, I don’t know who you are, but this was the best educational format I’ve ever seen. Great job. Thank you.

[@suhaimimazed1136]

Finally...a video! Very exciting to watch and knowledgable

[@alexanderlow6961]

Got it on immediate time for my vibrations class thank you!!!!!!!

[@szejie8439]

SAME HERE !

[@thehonestloaf3575]

Principles of physics 1 online?

[@Colton.ontheadventure]

Same. Exam this Thursday

[@Lowkeyyshorts]

Same haha 😂

[@gaulsaul4243]

I even learnt this today morning thank you!!!

[@poppyblop484]

The cover visual for this video is very engaging and never would I expect to want to relearn this topic again

[@gustavov.2940]

Man, your channel is amazing. Congrats on the work!

[@victorschannel1668]

That's brilliant that you started to do videos on dynamics. And it becomes even better considering that I will need to take dynamics course next semester and I am currently studying ODEs

[@mmgedi]

I can not thank you enough for this video. It is pure gold!

[@alexkempes1919]

You absolute gorgeous legend of a man!!! I have an upcoming final on this and FEA, I've watched both in under 3 days and it has been immensely helpful. Thaks so much!!! Keep it up!!!

[@yfardan1]

What a nice and clear video, It's really fantastic, I have never seen such an explanation. Thank you so much, go ahead and wishing you all the best

[@matteocolella412]

Wonderful!!!! The best video I have ever seen on dynamics. it would be nice to see something with fourier analysis and the Fourier transform related to seismic

[@GustavoLGNobre]

Your explanation is simply beautiful: cleaver, precise, comprehensive and elegant. Science is a beauty reunion of inteligence and perception.

[@MarKT777]

i just discovered this channel...bro this is like the eden for me... what a beatiful job you have done props to you

[@lavvukotic5248]

How this guy explains things is just exceptional !

[@pruthvirajkatkar7909]

Great animation and cleared concepts. Please make more videos on Vibrations, Finite element analysis, simulations, CAE

[@sunilas5365]

Awesome... As an automotive design Engineer. I bow to you for your excellent explaining video. ❤️ To support you!

[@athangsinhale4140]

Sir, the level of animation and the content is just god level. Can you also make a series of oscillations(wave optics)?

[@jamesmiles4089]

these videos are always such great quality and are extremely helpful

[@mani771403]

In 20 min you covered an engineering topic that took 6 hours to cover in class. Thank you so much! However, I want to thank you for the Curiosity Stream discount, it is my favorite❤❤❤.

[@shovkatsotivoldiev]

I can surely say that this is one of the best explanation of the vibration. Comprehensive and logical. Moreover, the excellent illustrations make the difficult things to become simpler. I regret that have found it after finishing my courses)

[@xturkishsa8092]

20 min video! Definitely gonna watch that, thank u for the effort in advance.

[@HDptt]

Masterpiece. We do need you upload these dynamics topic video to survive

[@manbeefcake]

Mode 3 is my dance technique... What slick video. I looove a soundly formed explanation.

[@fn3200]

The quality of this channel is over the top

[@worldingalaxy]

I have to watch this many times. Very useful for electrical engineering.

[@LabibianAMV]

Magnificently elaborated, I really admire your work.. keep going.

[@zacharymesecke9638]

Wow. First off, absolutely incredible video! Great quality and clear explanations. Secondly, I believe I have much studying ahead

[@DEVENDRAKUMAR-jc9zw]

Ultra-high quality videos. It provides the content for a semester.