To Master Physics, First Master the Harmonic Oscillator

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!

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:

[Alex-knlu]

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'.

[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.

[johnchessant]

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!

[barneycasting]

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!

[rodbarker]

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

[dailopez]

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!

[douglasstrother]

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!

[kennethmui]

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.

[arknightz]

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

[chadthunder]

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

[tangereenclaringbold]

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

[osamahebala]

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

[katg-gkox]

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

[tomi]

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

[zeroTorsion]

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

[praharmitra]

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

[LetsbeHonest]

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

[sharenrajenthiran]

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

[decreasing_entropy]

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.

[bwoy]

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