Equation of Motion for the Simple Pendulum (SDOF)

[@MdZeeshanAlamOfficial]

After watching all the KZbin videos i found this video helpful that has cleared my all doubt. Thank you so much sir from 🇮🇳

[@Romulo_Cunha]

Your channel is just amazing. I've been learning so much from it. Greetings from Brazil

[@natasham.r.6695]

You are literally saving my ass on my Mechanical Vibrations exame. Thank you so much!!!

[@rkgodara0200]

👍👍

[@lolazo21]

Brooo thanksa lot !!!!!! from the bottom of my heart

[@العراقيهالاصيل-ص8غ]

انت استاذ عظيم

[@Bronoulli]

In some solutions they include a phase shift beta in the argument of cosine…any chance you have a video on solving for beta?

[@Freeball99]

I talk about it in this video: kzbin.info/www/bejne/oqDZdaGqat6XqrM

[@SellusionStar]

Hi there! Let's consider this pendulum rotation around the Y axis (so the mass point is changing it's position inside the X-Z-Plane). Now: if I somehow rotate the rotation axis of the pendulum to an arbitrary axis; so I transform the (0,1,0) axis to eg (0.123,0.456,0.789). How can I now simulate the pendulum? Do I only have to calculate the resulting vertical component of the gravitational force? I hope my question is understandable. I try to program a pendulum simulation in 3D.

[@Freeball99]

The 3D equivalent of the simple pendulum is the spherical pendulum. This video should cover what you're looking for. kzbin.info/www/bejne/h6CTeopvZtmhn9k

[@Jack-in1fk]

What happens with the d/dt? (In lagrange) We dont use It? At least i didn't notice

[@Freeball99]

I did apply it. This is what gave us the double dot on top of θ in the first term.

[@nickpounders339]

what is J0 on the left equation?

[@Freeball99]

J0 = mL^2

[@ahmedibrahim4412]

Hello sir, When using LaGrange in this case, would it be wrong if I was to write the kinetic energy of the pendulum as 0.5*m*(theta_dot)^2? If yes, why?

[@Freeball99]

This is incorrect. KE can be written 0.5*J*(theta_dot)^2 where J = ml^2

[@jayaprakash1232]

Clear explanation tq sir And plz refer like ur channels particularly maths channels

[@Freeball99]

I'm a big fan of "Numberphile" and, especially, "Mathologer".

[@qingyangzhang887]

When you calculate the time derivative of partial derivative of Lagrangian, isn't there a factor of theta dot? Don't you need to take the derivative of the outer function, and then multiply it with the time derivative of theta dot?

[@Freeball99]

No, the chain rule doesn't apply here - it's not a function of a function. After the partial derivative of L w.r.t. theta_dot, I'm left with ml^2 theta_dot. Taking the time derivative of this w.r.t. time gives me ml^2 theta_ddot. The theta_dot you're referring to generally comes up when we differentiate trig functions w.r.t. time.

[@qingyangzhang887]

@@Freeball99 Thank you!

[@davepjandayan1910]

I need help, i have the given, length of the string and the mass and angel, it would really be appreciated.

[@Freeball99]

I assume you are trying to find the angle as a function of time and that you have been given the initial angle...in this case, IF THE INITAL ANGLE IS SMALL (less than about 10 degrees) then you can linearize the equation of motion and arrive at the well-known result for a linear pendulum which is, the period of vibration, T = 2π·SQRT(L/g) and the angle at any time, t is given by θ(t) = θo · cos (2π·t / T) where θo is the initial angle. If the initial angle is large, then you will require the nonlinear solution which involves solving the equations using numerical methods as I have shown in this video: kzbin.info/www/bejne/lZa9qoeEqc19fZY

[@arkadebghosh4169]

When I'm writing the equation of motion in Cartesian coordinates instead of polar,, I'm not getting x and y as periodic functions of time,,, but physically we know they are periodic,, please try to clear my doubt if u get it

[@Freeball99]

The solution to your equations of motion should be periodic in any valid coordinate system. The equations themselves should be 2nd order differential equations.

[@pulkitmahera4543]

Watch the following video for the graph plotting of the same problem using python language:- kzbin.info/www/bejne/gHamZ4tjhNGAo68

[@silentprayers728]

I get it. My confusion comes from when you combine one "type" of motion with another... like in my homework, the pendulum is connected to a spring in the horizontal direction. What then??

[@Freeball99]

Assuming the method of Lagrange's Equation...in that case, you would need to add to the potential energy, V, the contribution on the spring, which is equal to 0.5*k*x^2, where x is the deflection of the spring. This requires finding the deflection of the spring, x, in terms of the coordinate θ which will depend on where the spring is attached. For example, if the spring is attached to the rod (perpendicular to the rod) at a distance, d, from the hinge, then the deflection of the spring is x = d * sin θ. Then substitute into Lagrange's equation and you will end up with an additional term in the equation of motion.

[@franciscoxaviergonzalezrom4648]

Thank you so much, Sir! incredible presentation! How is the approach if I have a double pendulum in the Newtonian way??. I have already watched your double pendulum video using the Lagrangian way!

[@Freeball99]

I will have to make a video on this. It's a little more involved than the Lagrangian approach and too much to explain in the comments.

[@franciscoxaviergonzalezrom4648]

@@Freeball99 Thank you so much! I have already done with the Newtonian way (using radial and tangential coordinates) but I don't know if it is right... Thank you, Sir!

[@nickolasspagnolo7304]

he sounds like professer snape

[@saumya3065]

what software is this ?

[@Freeball99]

I am using an app called "Paper" by 53. I run it on an iPad Pro 13-inch and use an Apple Pencil. Connect the iPad to my Mac using USB and then perform video capture using Quicktime.

[@walaaalali3865]

the derative of cos is - sin and here we have -(-sin) = cos which change the result of L= ml^2 thata^2 - mgl sin thata

[@Freeball99]

Not sure I understand the point you are making.

[@PCgamerChannel]

I see these done but not a single example of it being used. Just equations wtf

[@Freeball99]

What sort of examples are you looking for? I have various animation videos which use the pendulum equations to display pendulum motion.