Eliminating Lambda to Solve Question 2(b) of Physics Homework

[Cosmossos]

Homework Statement

Hello ,
Please look at question 2 (b).
http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw05.pdf

I got that the lagragian is the potential energy (as in part a of the question)
How Do I eliminate the lamda so I can write the U (wave) as requested?
Or In Other word, How do I do b?
thanks

 

[jdwood983]

Homework Statement

Hello ,
Please look at question 2 (b).
http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw05.pdf

I got that the lagragian is the potential energy (as in part a of the question)
How Do I eliminate the lamda so I can write the U (wave) as requested?
Or In Other word, How do I do b?
thanks

Quick note: The Lagrangian is not the potential energy. It does have a potential term in it but it is not the potential energy; it is the difference between the kinetic energy and the potential energy.

The problem looks pretty straightforward. If you expand $\lambda$ to the two terms inside the bracket and then combine the two integrals, you should get the form requested.