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Problem 6. Consider particles of mass m attached through ideal springs of natural length L,, and elastic constant k. The edges of this chain of masses and springs are anchored to two rigid walls. A)Consider the case N=1, a single mass and two springs. Find the lagrangian in this case. B) Find the mass matrix M, and the potential matrix V. Use the algorithm seen in classes to find the normal frequencies of this problema. C) Repeat (a) and (b) for N=2 and write the matrices M. and V. in order. D) Repeat (a) and (b) for N=3 and write the matrices M. and V. in order. E) Write the matrices M, and V. for arbitrary N. 2 > eroo Rose erele er09