Suppose you are given n different springs. In which order should you connect them to unit masses so that the mass-spring chain vibrates the fastest? Does your answer depend upon the relative sizes of the spring constants? Does it depend upon whether the bottom mass is attached to a support or left hanging free? First try the case of three springs with spring stiffnesses c1 = 1. c2 = 2, c3 = 3. Then try varying the stiffnesses. Finally, predict what will happen with 4 or 5 springs, and see if you can make a conjecture in the general case.