Physics 68 Lagrangian Mechanics (18 of 32) Two Mass - Two Spring System

We will find the equations of motion of motion of a two mass-two spring system Lagrangian equations.

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[AQ-ejvv]

I truly cannot express how helpful these videos are..

Thank you very much.

[miralkumardesai]

As a Physics Educator, I highly appreciate your efforts professor.

[natorgas]

At 7:10, you're taking the partial derivative of the PE, not of the lagrangian. But actually you should take the partial of the Lagrangian with respect to x1, which would mean that there is a negative sign infornt of the expression(since it is KE - PE) that you are taking the partial derivative of. So in the end you'd have a different derivative. Can you explain that?

[TETTE]

Thank you for your video, which helped me solve a problem at work!

[pritamhait]

Sir, it's a wonderful explanation. You solve a difficult problem in the easiest way. It helped me a lot.

[katrinajadepajo]

Thank you so much sir! I would like to clarify on calculation of the partial derivative of L with respect to x2. I think only -kx1 will remain.

[mathlover]

Do the double pendulum with springs not strings. Once you get these down you can get pretty wild.

[fxs]

Hello, I suspect you have a small mistake with signs: you have to take derivative from Lagrangian (where PE has minus before it) but for simplicity you took derivative from PE itself, but did not take minus in L=KE-PE, so your equations will be correct with other signs. Also you have a typo: you wrote x squared where it should be x-sub-2, but after that you added it correctly to 2x-sub-2
Please correct me if I'm wrong, thanks!

[JH-uxre]

Really like these videos! I can review what I learned before and what I will learn soon or later!

[fizixx]

Love this method. I use to do this for systems I made up on my own. I'm gonna try and find the other videos for this problem with different masses and/or different k's. I wish my handwriting was a nice as yours. 🙂 ✏

[SumairaNaz-ed]

Hi sir I am from Pakistan and I really appreciate your cooperation 🎉❤❤❤❤❤ thanks for teaching us ❤

[etneide]

Thank you for your videos. At 10:09 you say correctly "x 2" but then you write "+ k x ^ 2". It is a "hand lapsus" because you complete correctly the equation, this just to inform you.

[СерикТабусов-ьн]

velocity supposed to be relative to each other V1 - V2 because velocity of each one of them will affect either one and the spring tensionnwon't have affectiont

[maximo]

gracias pelao, me hiciste la tarea de sld

[oneinabillion]

Omg thanks sir. I've been waiting for 1year 😂

[z_gm]

حينما اوجدنا البارشل كان يجب ان تستخدم من دالة لاكرانج، وليس من قبيل الطاقه
لان دالة لاكرنج اشارتها سالبه لذلك ستتغير الاشارات
هل حينما نستخدم الطاقه لايجاد البارشل يعطي نفس القيم المطلوبه؟
When we found the Barcel, it should have been used from the Lakrang function, and not from the energy, because the Lakrang function has a negative sign, so the signs will change. Is it when we use the energy to find the Parcel that it gives the same required values?

[sunahgamerl]

Really cool! Since the solution ended up being to differential equations relating the motion functions of the masses, would you then find the equation of motion for each mass by solving a system of differential equations?

[alexc]

I really love all your video, very useful, very easy to understand, they're all great, you're a great teacher. I just want to ask and confirm if a/ax1=kx1-kx2 is correct or not?

[michaelkouzmin]

I dare say at 10:15 you mixed superscript (^2) and subscript (#2) of x_second

[bangstar]

Why would newton's law not work here? It would simply be ma=k(x1-x2). Same as your answer