To Master Physics, First Master the Harmonic Oscillator
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- čas přidán 24. 01. 2022
- 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...
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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. - Věda a technologie
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.
Glad you liked it!
wait what? wow, 34 years ago.....may i ask what your age is sir?
@@ycombinator765 35
@@ycombinator765 No, you may not. 👳
@@ycombinator765 31
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'.
A man of culture, i see
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.
@@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.
“He died of -heart- harmonic oscillation failure.”
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!
Dude, that's our course material. I'll sure keep an eye out for the problem you mentioned
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.
Lennard-Jones potential! Used in solid state physics everywhere
Dude I just did that like 3 weeks ago, it's the Lennard-Jones potential!
okay this math is our assignment now. and I am facing problem 😢
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!
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
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
One dimensional physics kuda telsa ah ra niku???😃😆
@@chandu8081 what? Mind rephrasing your comment in English?
@@LetsbeHonest97 he's trolling you in telugu , he says "do you even know one dimensional physics?"
@@chandu8081 👏💀
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!
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
Very glad you liked it!
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!
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.
Thanks Kenneth!
Can't believe I've never seen the Taylor expansion trick you showed before. Very elegant.
Just found your channel, I see it's growing quite well! Thank you for the great explanations!
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
Been following your videos for a long time now! They are absolutely amazing and the animations are really well done!
Thanks Prahar! Much appreciated
Thanks for the great video, notes and animation. You really use an impressive way to explain these topics.
A complex concept explained elegantly! Amazing animations! Hope to see this channel grow!
Thanks Sharen!
These are great. Saw a lot of this in last semester's Jr/Senior level Classical Mechanics.
I am a mathematician from Spain and I enjoy how clear your videos explain complex topics
Thanks Pablo!
My students just did a lab on Simple Harmonic Motion today and I sent them this video! Really great overview!
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
There's so much content in under 10 minutes. Really appreciate it.
Brilliant explanation! This video contains main concepts in physics. Thank you for excellent video!
Beautiful video! This will help a lot thanks.
Elliott, you're fantastic, thank you, I'm benefiting a lot from your videos
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 ❤
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.
All your videos are so great and well explained I really enjoy every one of them. Greetings from Mexico 🇲🇽!
Thanks Daniel!
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.
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😊
Thanks Simran!
Wow, pls keep uploading these types of videos❤
I'm from Bangladesh.
& i'm also a physics lover.
Love the video.
It helped me a lot & cleared a lot of confusions
Thank you for your time and effort.
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!
Ω here ya go.
i really love ur videos.....amazing explanations and in detailed manner thankuu
ummm instant sub -- wish I had your videos when I was working through Morin and ofc Kleppner all those years ago -- well done!
Thank you!
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 🤓🤣
Another new tool learned today. Thank you.
Wonderful demonstration sir
I need more math intuition. I'm hopelessly lost. I liked this video. The narration was perfect
Perfect explanation
Really enjoy your videos
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 !
Thanks Emiliano!
@@PhysicswithElliot 😉
Damn nice explanation. Good work bro. Keep it up.
Amazingly explained.
excellent work 👍
great explanation thank you so much for your effort
Hope your channel will blow up someday keep it up
thanks a lot Elliot, your videos help a lot!
Happy it helped Shraddha!
Thank you so much, man!
This is a first class video.
Thank you very much
Well presented
Thanks for this really lucid explanation. 😊
Glad it was helpful Aditri!
thank you
excellent narrative easy presentation. great information
Man, Thank you so much
2:46 "How far did I pull it out" is definitely a very important question.
Me: Wait, it's all harmonic oscillators?
Physics: Always has been.
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. 😉
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
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
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!
Elliott, please make a series on Alternating current, electronics,
Woke up and saw this. You made my day!
Glad you liked it Agraj!
thank you soooooo much it really helped me
🙂
Nice work!
Thank you
Thanks my best lecturer
great class, good job!
Thanks Michele!
Thanks Elliot sir
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 :)
Thanks and welcome!
Lovely video, very impressive
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
Wonderful Video👌.
Brilliant ! Thanks a lot.
Thanks Carlos!
Nice one. Can we please have a part 2 on the quantum harmonic oscillator?
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)
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
Dr, please make videos about all of waves from beginner to advanced
A single HO is one thing, but many of them with some coupling is mind bending und fundamental.
Wow sir Amazing...
Thank u...
Great job 👍
Thanks Chirag!
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
eralr?
this was amazing thanks
Thanks Truman!
Proudest thing I have done in physics is finding time required to go to center of earth using shm
Great sir
You have a deep knowledge please upload atmospheric physics course, atmospheric wave
Please make many videos on classical physics so that many of 11th 12th grade students can understand ur videos
Check out the earlier videos in my "help room" playlist for more!
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?]
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
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
What an amazing video
Thanks Itachi!
He said innocuous and ubiquitous in the same sentence. Yes I needed spell check.
Broke my mind
Brilliant!
Thanks Umberto!
Every thing in our world is vibration(kinda harmonic)
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.
Can you please tell me which software are you using.... To create this video...
I like your content.
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
I have already suffered enough as student for underrating the harmonic oscillator...its literally everywhere.
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
9:43 is that the reason why qed during normalisation can simply ignore the higher order, even though its Taylor series actually add to infinity ?
Amazing
awesome video
Thanks Fei!