The Free Pendulum - Laplace Transform Solution + Phase Plane Arguments
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- เผยแพร่เมื่อ 31 ก.ค. 2024
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Today we apply the Laplace transform to the differential equation describing the motion of the frictionless free pendulum with small angle displacement! =) We apply our already established look up table inverse Laplace Transforms and arrive at the pendulum equation. After that we simplify it further using arguments in the phase plane and trigonometry on the stable center! Enjoy =) Video sponsored by Ridge btw!
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1+1=3 for large values of 1
This person physics.
1 has become so large it became 1.5
by this: 1=0 for large 1. thus, 1=0, qed
Papa Laplace has us covered with pretty much everything.
I don`t even know what these formulas are, but they look sexy as hell.
Based
yea fucc Fourier all my homies use e^-tx to apply normalization conditions at 0 and infinity
1:23 I couldn't watch the video past that point sorry. Too busy throwing up
xD
Hey papa, can you make a video on applied mathematics in biology? There's some really cool functions we use to determine the activity of enzymens and proteins, which are the Michaelis-Menten Equation(Hyperbolic relationship) and Proten-Ligand cooperativity (Sigmoidal relationship) respectively. There's also some cool Gibbs Free energy Equations we use that describe the membrane potentials that add concentration and electric charge. Thanks for your work!
Legend among us physics bois is that if you snort enough first-order Taylor approximations you start living in phase space
19:29 Thank you so much! That's right, that is the expression that we find in books and I was wondering how can I achieve that result, thanks to your video I now know where it came from.
It's amazing... I knew all the methods used except for the fi vs fi dot thingy, and I've never seen the cos and sin form of the pendulum which looks very convenient, I've always had to calculate the fi knot and was a pain in the ass D:
Good video as always Papa
As an electrical engineering student I love laplace transforms! That would be my choice method to solve that problem.
:)
Laplace and Fourier transforms are Electrical Engineer's love interests😄
These are the details my classical mechanics professor was scared to show me
haha :D
So was mine
Yup.
Please keep such nifty bois coming, it is delightful to watch you apply different methods of solving problems.
Why such few views! It is pure gold, even more so for physics enthusiasts like me! Keep it going man, no mere algorithm that fits into a margin can take down Flammable Maths!
Finally a video I understand as an engineering student, thank you.
Very good video too.
Woohoo another physics one! And I love the meme at the beginning. I chuckled cause that’s the smartass answer I would’ve given 😂😂
I actually just had a course about Euler Lagrange and how to solve for systems like this (and some more complex) . Nice to see again
Recent research has shown that the complexity of the meme is inversely proportional to the complexity of the video itself.
That wallpaper tho. Straight fire.
Subscribed for more applied mathematics!
OMEGALUL! Great video, great explanation. Finally some engineer-friendly content :')
Finally, a meme we can understand.
Not like the video :)
glad you have your sponsor, best of luck in the future
Great video! Any chance on covering the Chebyshev series for the harmonic oscillator?
Funny enough I actually have a pendulum lab in physics tomorrow so this is kinda dope, Thanks Papa Flammy!
Oh my god, I just watched a similar video you did two years ago!
Is it possible to solve this differential equation, if you use the cubic approximation of the sine function?
As a control engineer i love this kind of stuff mah dude
What if I account for large angles by making the sine function small
what a spicy video papa
dayum, harmonic approxilator with some black pepper?
Hi, Please can I get some resources on the topic of solving the pendulum equation using the Laplace transform I am studying mathematics and I need this topic for my graduation thesis Thanks
small phi ain't doing it form me, i usually assume it to be a whole number at least grahams number big (*2*pi + smol eps)
lets keep the channel alive!!
Now do it again with a frictional term and get a lovely spiral.
A little bit disappointed, I expected inverse of elliptic integral!
he already said in the video he would cover this in the next video
@@angelmendez-rivera351 And I have seen the next video! Exciting!
Hello. What about better approximation such as
x'' + g/l x - g/6l x^3 = 0
? 🙂
good luck solving that, your equation is still nonlinear then. You'd be better off using the sin(x)
Is it not possible to solve this differential equation without the small angle approximation? I saw this done by Taylor as well.
It is not possible to solve it exactly with known functions unless you use some special function.
Cool
S^2 + OMEGALUL^2
Do you watch twitch channels?
@@DarkRedZane ye
@@nanitech_ KEKW
If you took a shot every time he said Laplace transform you wouldn't survive the video.
Epic
whats the discord link?
Is there an operator that is not linear? Right now I can only think of linear ones, like the fourier transform operator, the differential operator, etc.
The composition operator is nonlinear. There are plenty of nonlinear operators, but you have never heard of them, because you only learn about them in advanced math courses for pure mathematics, because such operators are super useless in applied mathematics.
Are you going to quantize it next
Yes papappapapapiiiiii
Try to do the non approxilator free pendulum problem with boi Laplace xd
Haha, omega null sounds like omega lol
yo we do simple harmonic motion in our high school physics class but we don't use differential equations :(
Can you solve it exactly next time?
❤️
You engineer, you
I have one thing to ask papa flammy, which is more greater:
e vs. π
Can you figure out which is more better?
π > e
@@thedoublehelix5661 what if you approximated it? Then,
e ~ 3 and π ~ 3
Again, which is more better?
@@unknownpalooza8475 yeah, pretty the same thing. ⌈e⌉ = ⌊π⌋
@@IoT_ I agree with you, 👍
Hey papa where is the QNA
Like I said, this sunday! :)
What happened to the Q and A?
like I said, this sunday
@@PapaFlammy69 oh, i thought next vlog sunday would mean yesterday.
@@PapaFlammy69 could you repeate one more time? I've just forgot when you're going to have q&a
The first hhh
TH-cam algorithm goes against it‘s origin
Your Forward LT of nonlinear ODE is correct .But the Invert LT a bit INCOMPLETE and funny/missing 'Bode plot' ? Good try !
Where was this video 2 weeks ago when I had my control systems exam? Shame on u >:(
i wouldve alt f4ed if u said omega lol
Please use capital Xi next time. Phi/theta is pleb stuff
Trig identity assumed. Veiwers triggered.
The 8 people who disliked this are bad at math.
This comment has been left as an exercise for the reader
yeye
flakes
Physics isn't applied mathematics