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.