Can someone help me get the correct answer?

[clapper66]

Homework Statement

Homework Equations

The Attempt at a Solution

 

[Goddar]

Hi. What are the quantities you are using? (I_total, I₁, I₂ and l); what do they represent and how do you get these relations?
Do you know how to express the Lagrangian here?
If not, can you write Newton's 2nd law for each mass?