What is the physical interpretation of this calculus of variations problem?

[catpants]

It seems like a problem that a physicist would need to solve, but I can't wrap my head around the physical interpretation of it.

http://exampleproblems.com/wiki/index.php/CoV7

Also, why do they use u=c*x2? What is c in this case? It says "classical" so it can't be the speed of light, right?

 

[quietrain]

i believe it is a constant


something like 1/2 kx² for spring potential energy

 

[homology]

I agree, its clearly the Lagrangian for motion near an equilibrium such as the simple harmonic motion of a mass on a spring in the absence of gravity. They used the conserved quantity (energy) to solve the problem.