Lagrange EOM for 2 masses on a string

[stigg]

Homework Statement

Derive the equation of motion for the system in figure 6.4 using Lagrange's equations

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Homework Equations

m1=.5m
m2=m
strings are massless and in constant tension

Lagrange=T-V

The Attempt at a Solution

I currently have the kinetic energy as .5m₁y'₁² + .5m₂y'₂²

I am confused regarding the potential energy of the system. I understand each mass will have an m*g*y component associated with them but i am unsure how the tension plays into the potential energy. Once i have the potential energy for the system i can take it from there. Any advice would be greatly appreciated, thanks!

 

[ToBePhysicist]

Greetings,
So here is the how to 1:Short document:
Find me EoM!
2:Long video:

Note: I am going to get some sleep...If that is not what you asked for, please wait for someone else to answer you or @ToBePhysics so I can get to you when I am done doing things.

 

[stigg]

Hmm interesting video but I am afraid something is just not clicking for me with regards to this problem.

for the potential energy there will be a m₁gy₁ term and a m₂gy₂ term. I assume there must also be terms for the work done by the tension in the strings, but only the y components as these are only given one DOF each. That would give a Ty₁sin(θ₁) and Ty₂sin(θ₃) correct? assuming θ₁ is the angle between the left wall and that string and θ₃ is the angle between the right wall and the attached string.

My confusion is coming when i need to take into account the string attaching the two masses. Is my logic correct thus far?

 

[ToBePhysicist]

Hmm interesting video but I am afraid something is just not clicking for me with regards to this problem.

for the potential energy there will be a m₁gy₁ term and a m₂gy₂ term. I assume there must also be terms for the work done by the tension in the strings, but only the y components as these are only given one DOF each. That would give a Ty₁sin(θ₁) and Ty₂sin(θ₃) correct? assuming θ₁ is the angle between the left wall and that string and θ₃ is the angle between the right wall and the attached string.

My confusion is coming when i need to take into account the string attaching the two masses. Is my logic correct thus far?

W=P.E_f-P.E_i=K.E_f-K.E_i.
I don't know much about strings...But I am trying my best gathering resources that help..
Sometimes:
E.P.E=K.E

 

[stigg]

Hmm not sure that helps me a ton unfortunately.. i am reallly struggling to wrap my head around this potential energy problem.