The simple harmonic oscillator and the fundamental role of complex exponents for ODEs.
Next chapter on the Laplace Transform video:
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Timestamps:
0:00 – Intro
1:51 – Euler’s formula explained dynamically
9:27 – The harmonic oscillator
21:08 – General linear equations
22:47 – Motivating the Laplace Transform
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These animations are largely made using a custom Python library, manim. See the FAQ comments here:
Music by Vincent Rubinetti.
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3blue1brown is a channel about animating math, in all senses of the word animate. If you’re reading the bottom of a video description, I’m guessing you’re more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.
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Update: The next chapter is now live at https://youtu.be/j0wJBEZdwLsN
Thanks to all the patrons for early comments and helpful feedback on the draft.
Knowing Newton's viscosity law helps you understand the damping effect of fluids. Based on the law the shear stress (which causes opposite force) has a linear relationship with velocity
im looking for a study partner to work through precalculus and calculus. reply if interested.
Sorr, on your video there is one mistake, i think. It's on 15:50, that w= sqrrt(a2/a0) cause of we put it into an equation, we will get -a2*(a2/a0)e^iwt +a0e^iwt. And it doesn't equal to zero. I think, w should be equal to sqrrt(a0/a2). In that case zhen ze do a second derivative, we get -a2*(a0/a2) and that simplifies to -a0e^iwt which +a0e^iwt gives 0
THANK YOU SIR!! YOU ARE THE GOD!!👍👍👍
What a wonderful lesson! What program do you use to create these graphs and animations? Thank you.
this spring equation reminds me highschool physic courses when we were studying something like RST circuits (or something like that, dont actually remember the exact name).
It was a sine curve with decreasing peaks and i immediately had the intuition that the peaks decrease was following an negative exponential law, and somehow it felt logical (the less energy you have, the less the curve can decrease, like somehow the energy is the "acceleration" of the discharge) like it does in biology and nuclear decay. Now it makes even more sense because, in a way, it is kind of a spring (if you dont get it, thats fine, i understand myself)
Laplace transforms feel very limited to me because you can’t really take an inverse Laplace transform approximately. It either has an exact solution that someone has solved before, or it’s impossible.
❤❤❤❤❤❤
buen videito
Wie bringe ich die Zahn Medizin zusammen ?
Un video de media hora que se sienten menos de 5 minutos
The euler formula is the most erroneous equation in the history of math.
Your videos absolutely nail a very delicate but necessary balance of stepwise presentation of the needed bits with a continual tease of the incredible beauty just around the corner. That—whether in books, music, or shows—is what hooks people.
So much otherwise good content relies on secondhand recommendations “yeah the first 100 pages are dry but it gets good later”…you have to trust a friend’s advice or already know you like the creator; so many outsiders tire and put down the book not knowing what they missed. Likewise, too much media relies on endless attention-grabbing tease, without giving you anything of substance (the show Lost comes to mind); one’s excitement rapidly turns to disillusionment as they learn not to trust, not to hope for what they thought would arrive.
Every author or speaker could benefit from taking a page out of your book.
Grant, this is the third time I am watching this and what struck em was the benefit of listening; I couldn't watch the video so I turned up the sound and just listened and it made a huge difference. The comment from the young guy from India below, is priceless. Maybe you should make a series of these lectures that sequentially goes from the beginning to end in math, and make it a special series on the Khan Academy site?
You are great👍
I know this video's been up for a while, but I'm finally just watching it. That visualization at 6:35 is INCREDIBLE. Mind-blowing. 💜❤
Is this Patrick’s name?
Thank you for this video!
Thank you for this amazing explanation!
Every video of yours is truly dazzling!
Thanks for the video
This is all pure gold, but why so fast?!
i actually understand my classes now, this is insane. Thanks man
15:15 I mean, there’s the kinetic and potential energy?
The real genius of this channel isn't the incredible visualizations or the novel takes on ubiquitous mathematical concepts, it's that Grant seems able to perfectly anticipate the precise bafflement I'm about to feel, just as I'm about to feel it. I feel like an object being juggled, just as I'm about to be dropped, a hand appears and keeps me in the game.
This is the magnificent gift to the world heritage!
Awesome. I believe this knowledge is the missing link I needed when I studied Aeronautical Engineering 55 years ago.
Which grade should we understand this. I’m grade 5
Everything belong to me. Everything means everything.
Great job, this video was very useful!
Keep continuing contents like this bro it's helpful to lot of students schools and colleges don't teach us these stuffs so helpful content.
I could become a hostel warden in this academic year
I become a teacher for primary after a year with all the blessings
Good morning sir guruji
I learn this topic of Euler's formula for the spring.I must learn more number of lectures from this video Gurujis
From a senior citizen homes at ,Chengalput
Brilliant explanation.
4:24 continue roatating plz for no apparent reason
Honourable sir love from pakistan 🇵🇰 ♥
❤ @20:30 21/05/2026 17:18 ❤