The natural frequency (f) of a piezoelectric cantilever beam is described by the following equation: 1 3EI 2 m where E = Modulus of elasticity, / = Area moment of inertia, L = Length of cantilever beam, and m = Mass of proof mass (or end mass). The area moment of inertia for an arbitrary shape R with respect to an arbitrary axis (for example, x-axis) is related by: I, = [[ y dx dy. (a) What is the dimension of area moment of inertia? (b) If the thickness of a piezoelectric cantilever beam increases, does the natural frequency increase or decrease? (c) Both the thickness and width of a piezoelectric cantilever beam can change the natural frequency. Which parameter (thickness or width) will lead to the natural frequency change more significantly? Briefly explain your answer.