To Master Physics, First Master the Harmonic Oscillator

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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.physic...
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!
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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.physicswit....

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26 сен 2024

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Комментарии : 269

@burpleson 2 года назад

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 2 года назад

Glad you liked it!

@ycombinator765 2 года назад

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

@12388696 2 года назад

@@ycombinator765 35

@fuji_films 2 года назад

@@ycombinator765 No, you may not. 👳

@chromax1619 2 года назад

@@ycombinator765 31

@Alex-kn9lu 2 года назад

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 2 года назад

A man of culture, i see

@boonedockjourneyman7979 2 года назад

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 2 года назад

@@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 Год назад

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

@johnchessant3012 2 года назад

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 2 года назад

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

@manswind3417 2 года назад

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 2 года назад

Lennard-Jones potential! Used in solid state physics everywhere

@zombyMT 2 года назад

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

@varmygirl1183 Год назад

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

@Inndjkaawed2922 2 года назад

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 2 года назад

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

@Inndjkaawed2922 2 года назад

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

@gigachad1927 2 года назад

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

@ShanBojack Год назад

@@chandu8081 👏💀

@arknightz5046 2 года назад

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 2 года назад

Very glad you liked it!

@kennethmui88 2 года назад

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 2 года назад

Thanks Kenneth!

@rodbarker1017 2 года назад

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

@barneycasting8331 2 года назад

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 Месяц назад

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

@douglasstrother6584 2 года назад

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 2 года назад

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

@PhysicswithElliot 2 года назад

Thanks Pablo!

@sharenrajenthiran6899 2 года назад

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

@PhysicswithElliot 2 года назад

Thanks Sharen!

@praharmitra 2 года назад

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

@PhysicswithElliot 2 года назад

Thanks Prahar! Much appreciated

@Simran-qu5ny 2 года назад

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 2 года назад

Thanks Simran!

@dailopez5067 2 года назад

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!

@bwoy12345 Год назад

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

@katg-gk5ox 2 года назад

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

@rocketpie3300 2 года назад

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

@69erthx1138 Год назад

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 2 года назад

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

@dlrmfemilianolako8 2 года назад

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 2 года назад

Thanks Emiliano!

@dlrmfemilianolako8 2 года назад

@@PhysicswithElliot 😉

@seymaozkul9102 15 дней назад

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!

@HariharanAnnadurai 5 месяцев назад

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

@Jj-gi1sg 2 года назад

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 2 года назад

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 2 года назад

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!

@osamahebala6923 2 года назад

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

@doran321 2 года назад

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

@NoActuallyGo-KCUF-Yourself 2 года назад

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 Год назад

Ω here ya go.

@tomi6701 Год назад

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

@sleepygrumpy 2 года назад

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

@PhysicswithElliot 2 года назад

Thank you!

@decreasing_entropy3003 Год назад

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.

@shutupimlearning 2 года назад

Beautiful video! This will help a lot thanks.

@monabbar007 Год назад

Every thing in our world is vibration(kinda harmonic)

@tangereenclaringbold6921 2 года назад

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

@YolandaGarcia-dw3wl 2 года назад

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

@HS-vn9rt 29 дней назад

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

@mohitdhanik5274 2 года назад

Wow, pls keep uploading these types of videos❤

@trumanstew6223 2 года назад

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 2 года назад

eralr?

@agrajyadav2951 2 года назад

Woke up and saw this. You made my day!

@PhysicswithElliot 2 года назад

Glad you liked it Agraj!

@knutritter461 2 года назад

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. 😉

@jamesbond-th5bl Год назад

excellent work 👍

@banana6963 2 года назад

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 2 года назад

Thanks and welcome!

@aditric 2 года назад

Thanks for this really lucid explanation. 😊

@PhysicswithElliot 2 года назад

Glad it was helpful Aditri!

@omaralhafez5014 Год назад

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 ❤

@shraddhagore2435 2 года назад

thanks a lot Elliot, your videos help a lot!

@PhysicswithElliot 2 года назад

Happy it helped Shraddha!

@carlosayam 2 года назад

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 2 года назад

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

@voidisyinyangvoidisyinyang885 Год назад

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

@priyamshrivastava1016 2 года назад

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

@pranithkoochana401 2 года назад

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

@PhysicswithElliot 2 года назад

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

@coffeeguy.3438 2 года назад

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

@0MoTheG 2 года назад

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

@muqtarjamaegal6071 2 года назад

Energy equation must first

@chiragsharma1219 2 года назад

Great job 👍

@PhysicswithElliot 2 года назад

Thanks Chirag!

@DeepLyricist 2 года назад

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

@CarlosRamos-me7kg 2 года назад

Brilliant ! Thanks a lot.

@PhysicswithElliot 2 года назад

Thanks Carlos!

@falakniaz476 Год назад

Perfect explanation

@BariScienceLab 2 года назад

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

@PhysicswithElliot 2 года назад

Those moments are the best!

@alijoueizadeh2896 Год назад

Thank you for your time and effort.

@kabeerfcc4153 Год назад

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

@draftcypruss Год назад

Really enjoy your videos

@ItachiUchiha-wk3zm 2 года назад

What an amazing video

@PhysicswithElliot 2 года назад

Thanks Itachi!

@kirillvarchenko5691 2 года назад

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)

@padipucast 2 года назад

Well presented

@sarthmhatre3427 2 года назад

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 2 года назад

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 Год назад

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

@greatindianbuilder2491 2 года назад

Looks like you guys have a different symbol for Omega, it India we use a 'w' like looking symbol and the symbol you are using for Omega is also used for si unit of resistance.

@PhysicswithElliot 2 года назад

Upper vs lower case omega!

@wisnuape 2 года назад

Another new tool learned today. Thank you.

@hrperformance 2 года назад

This is a first class video. Thank you very much

@michelefabi1205 2 года назад

great class, good job!

@PhysicswithElliot 2 года назад

Thanks Michele!

@goopyt267 2 года назад

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

@user-ht6ql1rn3w Год назад

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

@waqasriaz4163 Год назад

Wonderful demonstration sir

@AM-gx3dy 2 года назад

Man, Thank you so much

@YouTubeFunHandle 8 месяцев назад

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

@memsuniverse Год назад

great explanation thank you so much for your effort

@idontevenhaveapla7224 9 месяцев назад

Thank you

@banilrajukvtamenglong6533 2 года назад

Thanks Elliot sir

@voidisyinyangvoidisyinyang885 Год назад

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

@michaelzap8528 5 месяцев назад

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.

@tsehayenegash8394 Год назад

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

@techconbd7661 2 года назад

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

@BRYDN_NATHAN 2 года назад

thank you excellent narrative easy presentation. great information

@upercoco 2 года назад

Brilliant!

@PhysicswithElliot 2 года назад

Thanks Umberto!

@cabdallahahmad7288 2 года назад

Thanks my best lecturer

@asdf8asdf8asdf8asdf Год назад

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?

@manishsramon Год назад

Thank you so much, man!

@Noah_Krakatoa Год назад

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

@vonzo55 Год назад

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

@gerrycrabtree3274 Год назад

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

@trumanstew6223 2 года назад

this was amazing thanks

@PhysicswithElliot 2 года назад

Thanks Truman!

@albertoreyabuelo2504 2 года назад

Broke my mind

@edu10th47 2 года назад

Why when proving that the total energy of a block in SHM is constant do we treat the displacement (x) in the potential energy equation with the Chain Rule, yielding du/dx=kxv (4:26), while in proving that force equals the negative of the slope of the potential energy we don't use the chain rule to differentiate the elastic potential energy (U)(4:46)?

@PhysicswithElliot 2 года назад

To find the rate of change with time you're taking the derivative with respect to t. To find the slope you're taking the derivative with respect to x

@user-vg7zv5us5r Год назад

11:10 due to F = dU/dx at 4:31 U'(s) = some F.

@notsoslimshady4315 Год назад

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

@umgeburstet8161 Год назад

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

@sanatkumargupta5368 2 года назад

thank you soooooo much it really helped me 🙂

@zetacrucis681 2 года назад

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

@samssams1619 Год назад

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 Год назад

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

@not_popskgaming8150 Год назад

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