To Master Physics, First Master the Harmonic Oscillator

It's hard to overstate how important the simple harmonic oscillator is in so many areas of physics. Almost every system is an oscillator near a stable equilibrium! Get the notes for free here: courses.physicswithelliot.com...
Of all the systems you'll study in your first physics class, the oscillations of a block attached to a spring are a subject you'll meet again and again throughout your physics education. The spring exerts a force on the block (sometimes called Hooke's law) that tries to push it back toward equilibrium, and the result is that the block oscillates around equilibrium in simple harmonic motion. But why is this simple system so prevalent throughout physics? The basic reason is that you can Taylor expand any potential energy function near a stable equilibrium point, and it will almost always look like the parabola of the simple harmonic oscillator potential energy!
Play with the animations: www.physicswithelliot.com/osc...
How to think of the potential energy like a hill: • The Trick that Makes U...
All about pendulums: • Everything You Need To...
Tutoring inquiries: www.physicswithelliot.com/tut...
If you find the content I’m creating valuable and would like to help make it possible for me to continue sharing more, please consider supporting me! You can make a recurring contribution at / physicswithelliot , or make a one time contribution at www.physicswithelliot.com/sup.... Thank you so much!
About physics help room videos:
These are intro-level physics videos aimed at students taking their first physics classes. In each video, I'll teach you the fundamentals of a particular physics topic you're likely to meet in your first classes on mechanics and electromagnetism.
About me:
I’m Dr. Elliot Schneider. I love physics, and I want to help others learn (and learn to love) physics, too. Whether you’re a beginner just starting out with your physics studies, a more advanced student, or a lifelong learner, I hope you’ll find resources here that enable you to deepen your understanding of the laws of nature. For more cool physics stuff, visit me at www.physicswithelliot.com.

[@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!

[@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!

[@chadthunder6915]

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

[@osamahebala6923]

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

[@rocketpie3300]

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

[@tangereenclaringbold6921]

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

[@LetsbeHonest97]

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???😃😆

[@LetsbeHonest97]

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

[@gigachad1927]

@@LetsbeHonest97 he's trolling you in telugu , he says "do you even know one dimensional physics?"

[@ShanBojack]

​@@chandu8081 👏💀

[@katg-gk5ox]

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

[@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!

[@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!

[@HariharanAnnadurai]

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

[@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

[@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!

[@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

[@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

[@sharenrajenthiran6899]

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

[@PhysicswithElliot]

Thanks Sharen!

[@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.

[@owen7185]

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

[@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

[@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 ❤

[@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.

[@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.

[@doran321]

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

[@zeroTorsion]

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

[@PhysicswithElliot]

Thanks Pablo!

[@shutupimlearning]

Beautiful video! This will help a lot thanks.

[@mohitdhanik5274]

Wow, pls keep uploading these types of videos❤

[@alijoueizadeh2896]

Thank you for your time and effort.

[@YolandaGarcia-dw3wl]

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

[@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 🤓🤣

[@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

[@DeepLyricist]

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

[@goopyt267]

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

[@wisnuape]

Another new tool learned today. Thank you.

[@danieldiaz-xi5bw]

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

[@PhysicswithElliot]

Thanks Daniel!

[@notsoslimshady4315]

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

[@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. 😉

[@manishsramon]

Thank you so much, man!

[@hrperformance]

This is a first class video. Thank you very much

[@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!

[@Mayank-mf7xr]

Amazingly explained.

[@falakniaz476]

Perfect explanation

[@memsuniverse]

great explanation thank you so much for your effort

[@kycb101]

Hope your channel will blow up someday keep it up

[@waqasriaz4163]

Wonderful demonstration sir

[@kabeerfcc4153]

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

[@AM-gx3dy]

Man, Thank you so much

[@BRYDN_NATHAN]

thank you excellent narrative easy presentation. great information

[@zetacrucis681]

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

[@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!

[@0MoTheG]

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

[@draftcypruss]

Really enjoy your videos

[@jamesbond-th5bl]

excellent work 👍

[@sanatkumargupta5368]

thank you soooooo much it really helped me 🙂

[@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

[@padipucast]

Well presented

[@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 😉

[@banilrajukvtamenglong6533]

Thanks Elliot sir

[@shraddhagore2435]

thanks a lot Elliot, your videos help a lot!

[@PhysicswithElliot]

Happy it helped Shraddha!

[@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)

[@aditric]

Thanks for this really lucid explanation. 😊

[@PhysicswithElliot]

Glad it was helpful Aditri!

[@techconbd7661]

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

[@tsehayenegash8394]

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

[@pramodlamichhane9266]

Nice work!

[@coffeeguy.3438]

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

[@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!

[@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?

[@agrajyadav2951]

Woke up and saw this. You made my day!

[@PhysicswithElliot]

Glad you liked it Agraj!

[@cabdallahahmad7288]

Thanks my best lecturer

[@michelefabi1205]

great class, good job!

[@PhysicswithElliot]

Thanks Michele!

[@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

[@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!

[@benwinstanleymusic]

Lovely video, very impressive

[@YouTubeFunHandle]

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

[@akshaysingh5469]

Wow sir Amazing... Thank u...

[@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?

[@CarlosRamos-me7kg]

Brilliant ! Thanks a lot.

[@PhysicswithElliot]

Thanks Carlos!

[@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

[@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 🤔.

[@idontevenhaveapla7224]

Thank you

[@anuraagchandra2548]

Wonderful Video👌.

[@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

[@trumanstew6223]

this was amazing thanks

[@PhysicswithElliot]

Thanks Truman!

[@vonzo55]

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

[@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

[@nishantkumarsharma8934]

Hello, can you tell me which software you use to create this type of videos. Also can you suggest any reference tutorial, like how to create these type of animations

[@chiragsharma1219]

Great job 👍

[@PhysicswithElliot]

Thanks Chirag!

[@albertoreyabuelo2504]

Broke my mind

[@not_popskgaming8150]

10:46 when I did my lab I didn’t now h=l-lcostheta and I had an equation around 5 times as large, while I was simplifying there was even a half angle cosine in there and I did arrive at l-lcostheta

[@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

[@upercoco]

Brilliant!

[@PhysicswithElliot]

Thanks Umberto!

[@BariScienceLab]

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

[@PhysicswithElliot]

Those moments are the best!

[@tejas6211]

8:55 We can reproduce the exact function only in the vicinity of the point about which the Taylor series is expressed. Please correct me if I am wrong.

[@pitiwatkittiwimonchai4656]

Great sir

[@user-ht6ql1rn3w]

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

[@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!

[@ItachiUchiha-wk3zm]

What an amazing video

[@PhysicswithElliot]

Thanks Itachi!

[@akshaysingh5469]

Can you please tell me which software are you using.... To create this video...