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Construct Lagrangian for the given system (Mechanics)

mathkid
in Homework Help

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Hello!

I have some problems with constructing Lagrangian for the system (attached files).

I made an attempt to find the Lagrangian (attached files), but I'm not sure if I did everything correctly. I also didn't use l, that is given in the conditions, to construct Lagrangian. Please help me point out my mistakes.

I'll appreciate any help. 

20171205_192712-2.jpg

20171205_192705-1.jpg

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