this is great. I have gone through lots of videos and materials on this oscillation of the pendulums for a week now, and I just could not understand why the equation is like that. this really helps me a lot. thank you. you know what, you earned another subscriber
This. I'm sharing this. SO well explained and your explanations are the perfect level, anything more and it would be repetitive (so you use the links to other videos). 10/10 good job and ty
The period of a pendulum is not dependent on its inital angle. The differential equation that governs pendulums is θ ' ' = - g/L * sinθ the larger the initial angle, the faster the pendulum will pursue a lower point. The period of a pendulum is given by T = 2π√(L/g) there is zero angle dependence, and nothing special about 30⁰. I'm not sure what you mean by "fundamental foundations to the basics of geometry" nothing in math is significant beyond our understanding, after all we invented the subject and it's contents. However, some constructs are useful. 30⁰ is useful for geometry and calculus, but not meaningful in any philosophical or cosmological way.
I use OBS to screen capture while writing on a simple digital pad in SmoothDraw, graphics are imported from MS Word after inverting in IrfanView, and I edit (cutting out stuttering and pauses) in Adobe Premiere Pro.
That's an interesting idea . . . do you mean a simple model of "g" getting smaller with altitude, or something more complex (correcting for the local mass of the mountain as well). I read somewhere that precise measurements of "g" even vary over the surface of the Earth due to very local densities of mineral deposits, etc. I wonder if the mountain under your feet makes a significant percent difference compared to the change due to altitude.
@@ZaksLab i wasnt really talking about so many variables since they dont come in my exams. I was actually talking about the maths that appears in the university admission exams .(related to pendulum being used to measure the height of the mountain or radius of the moon when the time period is given)
Here's one from the archives that covers parts of your problem: ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-EC1-TXsOEVE.html We solve for g at the end. This is really the same class of problem, just solved for g at the end instead of relating to radius using g=GM/r^2.
You can use the period formula with the small angle approximation, as long as you are OK with a little bit of error (about 3% difference between sin(theta) and theta). Getting the most general solution is a more advanced question (upper div/graduate level), and I don't recall exactly what happens there. It requires solving an elliptic integral if I remember correctly. z
The c1 and c2 are there because the general solution of a 2nd order differential equation must have two arbitrary constants. The two functions with sine and cosine are linearly independent solutions of the equation, and their linear combination gives the general solution of the original equation. These two constants give you the flexibility to match two initial conditions in order to nail down the particular solution of the equation. For example, I could give you theta(0)=pi/12 and theta'(0)=0 (start from rest at an angle of pi/12), and you'd be able to solve for the c's and specify the equation of motion for theta for all moments in time. To get a better sense for the differential equations here, check out the derivation of the general solution for the simple harmonic oscillator, which I meant to post as a "card" in this video, but apparently forgot to do! ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-yf6VD1xr7Bs.html
I learned this in 9th grade. Please tell me at ages do people from other place study this. I really liked your video I have been curious about this formula since 6th grade. Extremely helpful if you ask me
Thanks! I know . . . a viewer pointed this out last Spring, and I learned how to set it correctly in my editing software. Unfortunately RU-vid doesn't allow volume adjustments to existing videos anymore, and I'm hoping that option comes back soon! -- Zak
@@calvinjackson8110 It's on my to-do list, but the number of videos that need volume adjustment is about 300-400 videos from last year! Each video would take about 30 minutes to adjust volume and re-render, then about an hour of description, tags, etc., for a total of about 500 hours of time I won't have until summer '22. I super hope RU-vid gets that volume adjustment tool back this year! Tough lesson as a video production noob this year: adjust volume to about - 6dB peak even if it sounds great in headphones! -- Zak
Why use two meters? The Egyptians did not have meters. The meter was invented in 1791. Not only were the Egyptians cosmological geniuses but clairvoyant too!
d/dt is the time derivative operator, d^2/dt^2 is the second time derivative, and applying this to theta means we're looking at the angular acceleration z
@@mikaelafrias7786 are you talking about the differential equation part? This is a second order differential equation relating angular position and angular acceleration, and that requires some background to know how to solve (linked in the video to show how you guess the trig function solutions to this type of ODE). But unless I'm mistaken on what you mean by "d", it sounds like you don't have the calculus background, and this video is using ideas from the end of calculus II. If you're in a trig based physics course, the period formula is used without proof, and you can always safely assume the angle is "small enough" for the standard period formula to work.
