e are choosing material for a round rod. The material must be a metal or alloy. The length of the rod must be close to 1 m, and its cross-sectional diameter must be between 1 mm and 3 mm. Its natural frequency of vibration, f, should be as low as possible. (a) Clearly list the constraints, objective, and free variables. (b) What is the performance index of the material? (c) What are the best 2 material candidates?