Reconsider the massive string exercise above using Lagrange multipliers in order to express the constraints; i.e., the length of the string and the positions of the endpoints.

Exercises Q4 

In the calculation of bent rays (Sect. 2.2.2) or the massive string above, show that the quantity Г(z) = r/√1 + ˙r (z)2 is constant along the path (or string). From that observation, deduce the solution of the problem.