To Master Physics, First Master the Harmonic Oscillator

[@Alex-kn9lu]

if I was asked to describe physics in one sentence I'd say 'Everything is a harmonic oscillator if you're brave enough and everything converges if you wait long enough'.

[@Leomenxd]

A man of culture, i see

[@boonedockjourneyman7979]

How about this “find a guy named Feynman.” Too easy I guess. I’m absolutely sure you’d do better. Feynman was such a bore. The problem was he made you laugh so hard it was impossible to forget his reasoning. But I’m absolutely sure you’d do better.

[@ChristAliveForevermore]

@@boonedockjourneyman7979 all of Feynman's contemporaries, like Freeeman Dyson, Leonard Susskind, and Murray Gell-Man, all claimed Feynman was a creative genius and computational savant. His sense of humor and social skills were what contrasted his freaky mathematical ingenuity and physical intuition. The *early* 20th century physics legends, figures like Bohr, said Feynman was like Paul Dirac, but human (since Dirac was basically Rain Man in the 20th century physics community). Don't downplay Feynman's role in physics or his extreme cleverness just because he either intimidates you or appears too foolish to be a genius. Genius comes in many guises, not all of them appealing.

[@Democratic_Republic_of_Iacon]

“He died of -heart- harmonic oscillation failure.”

[@burpleson]

Very nicely done. Although I received my physics PhD 34 years ago, I enjoy watching your clear explanations. I'm sure many students are benefiting from your efforts. Thanks.

[@PhysicswithElliot]

Glad you liked it!

[@ycombinator765]

wait what? wow, 34 years ago.....may i ask what your age is sir?

[@12388696]

@@ycombinator765 35

[@fuji_films]

@@ycombinator765 No, you may not. 👳

[@chromax1619]

@@ycombinator765 31

[@johnchessant3012]

I remember I was so proud for figuring out the "Taylor expand around the minimum and compare with a simple harmonic oscillator" trick by myself. There was an exercise in Kleppner/Kolenkow about some atomic potential which had 6th powers and 12th powers and I was at a loss for awhile before coming up with it. Great video!

[@amarnathck574]

Dude, that's our course material. I'll sure keep an eye out for the problem you mentioned

[@manswind3417]

I guess you're referring to the question where U(x) is modeled as a/x^6 - b/x^12 right? And we probably had to fibd the equilibrium point which is easy, and some other question also followed.

[@s3cr3tpassword]

Lennard-Jones potential! Used in solid state physics everywhere

[@zombyMT]

Dude I just did that like 3 weeks ago, it's the Lennard-Jones potential!

[@varmygirl1183]

okay this math is our assignment now. and I am facing problem 😢

[@barneycasting8331]

I just got my tenure as professor in a US college, I am a researcher but have to teaching students. I need to admit that I am not a good Physics teacher. Your videos saved me from getting fired from the job, thanks a million!

[@rNT-lf2hf]

Wow!!! How Honestly criticized to Self.. I am not good of.. Physics.. 🙏🙏

[@arknightz5046]

Great video you made here, I study physics as an undergraduate and I failed this part last year so… I’m glad I found your channel ! pure treasure

[@PhysicswithElliot]

Very glad you liked it!

[@Inndjkaawed2922]

Dude, you hit the nail on the head with this video. During my entire time in college, I was only able to midly link everything that I studied with one dimensional harmonic oscillator. Now, I realised why I was unable to do well in college. I'm trying to get back into Physics to pursue a PhD. Let's see how far I get with a renewed approach

[@chandu8081]

One dimensional physics kuda telsa ah ra niku???😃😆

[@Inndjkaawed2922]

@@chandu8081 what? Mind rephrasing your comment in English?

[@gigachad1927]

@@Inndjkaawed2922 he's trolling you in telugu , he says "do you even know one dimensional physics?"

[@ShanBojack]

​@@chandu8081 👏💀

[@rodbarker1017]

My Father was a charterd civil engineer and a deffinate wiz with reinforced concrete. e was always banging on about SHM and how it got into everything arround us....Back in the day I was not a little behind the curve, having quite marked ADHD & OCD. in the 50"s I was just put down as Thick.... Well a lot of water under the bridge and NO not as dosey as they all thaught. How I wish I had the knowledge and understanding I now have to recognise the brilliance of Pop. We could hace rocked. I cant thank you enough you have helped me realise I may not be a dope and have something to offer. and hoe brilliant he was. However I can now get behind my two grandkids who are confirmes exceptional and in special schooling. I now know where it comes from. Just thanks a million

[@kennethmui88]

Fantastic Video! Great Animations/Simulations, Super clear and concise and you show the steps in the math! Absolutely the best. I never saw the simple harmonic motion explained like this.

[@PhysicswithElliot]

Thanks Kenneth!

[@chadthunder6915]

Can't believe I've never seen the Taylor expansion trick you showed before. Very elegant.

[@douglasstrother6584]

That goofy potential energy profile you sketched could be scoped-out using spectroscopy for an atomic or condensed matter example. The curvature of each of the local minima would generate different energy states and spectral lines. The SHO is everywhere!

[@zeroTorsion]

I am a mathematician from Spain and I enjoy how clear your videos explain complex topics

[@PhysicswithElliot]

Thanks Pablo!

[@bwoy12345]

I have a degree in math and physics and I only now understand what a Taylor series does. You just made sense of so much that I know

[@dailopez5067]

I just found your channel yesterday and how I wish I found it when I was getting my BSc in physics. Amazing work at explaining things clearly!

[@YolandaGarcia-dw3wl]

I need more math intuition. I'm hopelessly lost. I liked this video. The narration was perfect

[@NoActuallyGo-KCUF-Yourself]

1. I've never seen the upper-case _Omega_ used here. 2. Omega is not the natural frequency; it is the angular frequency. It has units of radians per second, because sine and cosine operate on angles, not number of cycles. Angular frequency, omega, equals 2pi×f. Where frequency, f, is in units of cycles per second (or hertz). Dimensional analysis matters!

[@user-vg7zv5us5r]

Ω here ya go.

[@Simran-qu5ny]

Please make a video on the forced harmonic oscillator and moment of inertia....your video and way of explanation is so amazing I am really glad to see your videos😊

[@PhysicswithElliot]

Thanks Simran!

[@HariharanAnnadurai]

There's so much content in under 10 minutes. Really appreciate it.

[@md.taohidislamtoha3615]

I'm from Bangladesh. & i'm also a physics lover. Love the video. It helped me a lot & cleared a lot of confusions

[@sharenrajenthiran6899]

A complex concept explained elegantly! Amazing animations! Hope to see this channel grow!

[@PhysicswithElliot]

Thanks Sharen!

[@69erthx1138]

I would have loved to have a physics teacher like you back 35 years ago. Looked at your other videos as well. You give a very clear description of quantum mechanics and field theory. Really like the comment, "...you'll see this behavior in everyday life if you PAY ATTENTION." LOL 🤓🤣

[@knutritter461]

Chemistry here: You need it in chemical analytics as well. Molecules do not just rotate, they vibrate as well! And for the vibration the harmonic oscillator is used as a starting model. Later you will move on to the inharmonic one and after that: You combine those vibrations while something is rotating as well! 😉 When the vibration stretches the bond it will rotate slower... when the bond gets shorter the molecule will rotate quicker. 😉

[@dlrmfemilianolako8]

Very beautiful . Taylor series is the best series to make an approximation of any function that helps us to make derivative and integrals with more simplicity. Taylor series with fourier analasys ( series and transform ) help a lot when take for the first time Quantum Mechanics . Thank you so much !

[@PhysicswithElliot]

Thanks Emiliano!

[@dlrmfemilianolako8]

@@PhysicswithElliot 😉

[@seymaozkul9102]

Thank you sir! You helped me a lot to learn the subject. To be honest, I never realized that the up and down motion of the ice I put into the lemonade was an oscillating motion. Or that shirts hanging on hangers are simply oscillators as they swing. Thank you, best regards!

[@decreasing_entropy3003]

Extremely well explained! Combining high school Physics with a very measured amount of undergrad Physics with a very properly worded script to make a strong video on the harmonic oscillator.

[@praharmitra]

Been following your videos for a long time now! They are absolutely amazing and the animations are really well done!

[@PhysicswithElliot]

Thanks Prahar! Much appreciated

[@tangereenclaringbold6921]

My students just did a lab on Simple Harmonic Motion today and I sent them this video! Really great overview!

[@M1551NGN0]

Harmonic motion is one of my favourite topics in Physics due to it eventually setting up the base for the study of mechanical waves and then EM waves, which has direct connections to Astrophysics and I love astrophysics. It's also surprisingly easy if we consider how much of its portion is present in 11th grade textbooks.

[@katgirl3000]

These are great. Saw a lot of this in last semester's Jr/Senior level Classical Mechanics.

[@rocketpie3300]

Just found your channel, I see it's growing quite well! Thank you for the great explanations!

[@danieldiaz-xi5bw]

All your videos are so great and well explained I really enjoy every one of them. Greetings from Mexico 🇲🇽!

[@PhysicswithElliot]

Thanks Daniel!

[@0MoTheG]

A single HO is one thing, but many of them with some coupling is mind bending und fundamental.

[@tomi6701]

I just learned about harmonic oscillation in my high school, but your video really blows my mind about many other stuff. Thank you very much :D

[@pranithkoochana401]

Please make many videos on classical physics so that many of 11th 12th grade students can understand ur videos

[@PhysicswithElliot]

Check out the earlier videos in my "help room" playlist for more!

[@kabeerfcc4153]

Elliott, please make a series on Alternating current, electronics,

[@Jj-gi1sg]

Fantastic animation and explanation! I am not familiar with calculus in physics as I am in highschool but I will always wonder: would another term in term taylor series make our job so much harder? I would think we could add it for the shake of realism

[@PhysicswithElliot]

The more terms you add the better you'll match the actual function over a wider range, but the more complicated the equation will become

[@tiddlywinks497]

In 2D systems, we sometimes need these higher-order terms to properly identify the characteristics of these equilibrium points. This is a really interesting subject and you should check out Steven Strogatz' book 'Nonlinear Dynamics and Chaos' in the future!

[@monabbar007]

Every thing in our world is vibration(kinda harmonic)

[@agrajyadav2951]

Woke up and saw this. You made my day!

[@PhysicswithElliot]

Glad you liked it Agraj!

[@BariScienceLab]

My God! 7:35 was a revelation for me!

[@PhysicswithElliot]

Those moments are the best!

[@osamahebala6923]

Thanks for the great video, notes and animation. You really use an impressive way to explain these topics.

[@DeepLyricist]

2:46 "How far did I pull it out" is definitely a very important question.

[@user-ht6ql1rn3w]

Proudest thing I have done in physics is finding time required to go to center of earth using shm

[@doran321]

Brilliant explanation! This video contains main concepts in physics. Thank you for excellent video!

[@michaelzap8528]

Oh my God, heroes see the same thing. When I decided to teach my son physics, the first thing I did was teach him solar system, Euler's formula, the Fourier transform, basically the circle.

[@voidisyinyangvoidisyinyang885]

this vid cuts through so much physics math misunderstanding it's ridiculous. How many times have I opened a physics textbook to stare at the harmonic oscillator problems, wondering what all the fuss was about? Hilarious. ONLY this vid explains the secret! thanks

[@shutupimlearning]

Beautiful video! This will help a lot thanks.

[@daniellim5037]

the stock image used as the background of this video had me thinking my computer screen was dirty

[@davel7037]

I have already suffered enough as student for underrating the harmonic oscillator...its literally everywhere.

[@trumanstew6223]

I love this upper level stuff do you think u can go over how one would deal with using eralr and complex solution to solve harmonics

[@PhysicswithElliot]

eralr?

[@sleepygrumpy]

ummm instant sub -- wish I had your videos when I was working through Morin and ofc Kleppner all those years ago -- well done!

[@PhysicswithElliot]

Thank you!

[@mohitdhanik5274]

Wow, pls keep uploading these types of videos❤

[@hrperformance]

This is a first class video. Thank you very much

[@zetacrucis681]

Nice one. Can we please have a part 2 on the quantum harmonic oscillator?

[@asdf8asdf8asdf8asdf]

Your graph of the complex potential with nearby equilibria at different levels makes me wonder how hard it would be to extend this presentation to include a bit of catastrophe theory?

[@waqasriaz4163]

Wonderful demonstration sir

[@carlosayam]

Great video Elliot. By the way, the 2nd Taylor expansion is also good at unstable equilibrium points. So, maybe a good idea to explain what the harmonic "oscillator" looks like in that case as well [it won't behave like an oscillator, hence my quotes - what sort of "spring" will it have?]

[@PhysicswithElliot]

Thanks Carlos! When you tap a particle away from an unstable equilibrium (which remember is like a ball at the top of a hill), it will roll down the hill and in general travel far away from where it started. So the quadratic approximation isn't very useful here, because the particle will quickly leave the region where that parabola was a good approximation to the potential

[@priyamshrivastava1016]

Hey !! Can you tell me through with app you do the animation work ?? it looks so beautiful and interesting🤩 , I also want to made something like these for college presentation

[@probablyshadman]

Dr, please make videos about all of waves from beginner to advanced

[@banana6963]

This was great. I was preparing this chapter for a week and just finished it today. I've heard about the Taylor expansion trick but never understood from the explanations from the very few videos I could find on it. This helped me a lot. Liked and subbed. Thanks for your efforts :)

[@PhysicswithElliot]

Thanks and welcome!

[@wisnuape]

Another new tool learned today. Thank you.

[@falakniaz476]

Perfect explanation

[@jamesbond-th5bl]

excellent work 👍

[@tsehayenegash8394]

You have a deep knowledge please upload atmospheric physics course, atmospheric wave

[@aditric]

Thanks for this really lucid explanation. 😊

[@PhysicswithElliot]

Glad it was helpful Aditri!

[@owen7185]

Elliott, you're fantastic, thank you, I'm benefiting a lot from your videos

[@muqtarjamaegal6071]

Energy equation must first

[@umgeburstet8161]

also, taylor series can have a finite radius of convergence, so the series might diverge no matter how many parts you may add to the sum

[@draftcypruss]

Really enjoy your videos

[@coffeeguy.3438]

Me: Wait, it's all harmonic oscillators? Physics: Always has been.

[@samssams1619]

In case anyone is gonna see this: at approximately 8:30 he is using u‘(0)x but u‘(0) and every higher derivative should just be 0 aswell therefore an approximation around the equlibrium point would only be u(0). First question: am i right with this? Second question: why isnt he using another formula for the taylor series when not developing his function at 0 but at 0+a (with a being the offset)? As far as im concerned the formula then looks different.

[@voidisyinyangvoidisyinyang885]

Hi [fill in blank] -- When you're near the equilibrium point, the higher powers of x will be smaller and smaller, because they're powers of a tiny number. Take a look at my video on Taylor series for more explanation

[@kirillvarchenko5691]

Interestingly that we can do the same trick for the minimum of U_{eff} from the video about orbits and then get the same result from the exact formula for r(\theta) by Taylor expansion at \epsilon=0 (which apparently corresponds to low energy, almost "harmonic oscillator" case)

[@omaralhafez5014]

You are great Elliot! Thanks for such brilliant explanation and interpretation of modern physics ❤ I really love what you are presenting. And the content is useful and .... And just great ❤

[@padipucast]

Well presented

[@HS-vn9rt]

You are awesome. Thank you so much for top quality lessons.

[@alijoueizadeh2896]

Thank you for your time and effort.

[@albertoreyabuelo2504]

Broke my mind

[@cabdallahahmad7288]

Thanks my best lecturer

[@Mayank-mf7xr]

Amazingly explained.

[@YouTubeFunHandle]

Great explanation. One minor point, if the force reference point to the left, wouldn’t F be kx instead of -kx?

[@shraddhagore2435]

thanks a lot Elliot, your videos help a lot!

[@PhysicswithElliot]

Happy it helped Shraddha!

[@notsoslimshady4315]

Damn nice explanation. Good work bro. Keep it up.

[@ItachiUchiha-wk3zm]

What an amazing video

[@PhysicswithElliot]

Thanks Itachi!

[@michelefabi1205]

great class, good job!

[@PhysicswithElliot]

Thanks Michele!

[@krishnapadanaskar3329]

From India , 😊

[@voidisyinyangvoidisyinyang885]

can you do a vid on how the quantum potential energy is in the real part of the Schroedringer equation but originates from noncommutative nonlocality as explained in Moyal algebra? thanks

[@sarthmhatre3427]

Can you please explain the velocity and pressure relation in the Bernoulli's equation, i mean not mathematically but physically like how does more velocity actually makes the pressure go down in fluids.

[@PhysicswithElliot]

I will add Bernoulli's equation to my list of potential topics! It's essentially the statement of conservation of energy for a simple fluid, where the pressure force produces an extra term in the potential energy

[@user-vg7zv5us5r]

@@PhysicswithElliot hehe, "potential" playlist. All about them potential.

[@goopyt267]

i really love ur videos.....amazing explanations and in detailed manner thankuu

[@chiragsharma1219]

Great job 👍

[@PhysicswithElliot]

Thanks Chirag!

[@gerrycrabtree3274]

He said innocuous and ubiquitous in the same sentence. Yes I needed spell check.

[@manishsramon]

Thank you so much, man!

[@AM-gx3dy]

Man, Thank you so much

[@Noah_Krakatoa]

Highly recommend the book Waves and Oscillations by Walter Fox Smith to dive deeper into this topic; there’s some errata to the book published online, but overall is excellent

[@rajinfootonchuriquen]

Maybe one could define a piece-wise potential aproximation using parabolas for the steady points

[@memsuniverse]

great explanation thank you so much for your effort

[@CarlosRamos-me7kg]

Brilliant ! Thanks a lot.

[@PhysicswithElliot]

Thanks Carlos!

[@imaginaryuniverse632]

Would the stable equilibrium point be the same as a barycenter? Would it's position be a Planck length? Hey I just found this channel it does a good job of letting you know what you need to know even though I don't know half of what it says 🤔.

[@trumanstew6223]

this was amazing thanks

[@PhysicswithElliot]

Thanks Truman!

[@idontevenhaveapla7224]

Thank you

[@vonzo55]

I just got an idea for my next Max/MSP little instrument

[@ramansb8924]

Can you do video about tensors??

[@PhysicswithElliot]

Probably! At the very least I definitely want to talk about the electromagnetic field strength tensor in the near future and write down the action for electromagnetism

[@ramansb8924]

@@PhysicswithElliot that's awesome, waiting ✨

[@pramodlamichhane9266]

Nice work!