Find the sectional lift and moment coefficients taken about the midchord for the airfoil given in Problem 3.2 undergoing a simple harmonic motion \(h=\bar{h} e^{i \omega t}\).

Problem 3.2

An airfoil is given by a parabolic camber line, i.e., \(z_{a}=-\left(a / b^{2}\right) x^{2}\). Find: 

(i) sectional lift coefficient, 

(ii) center of pressure, 

(iii) aerodynamic center, at zero angle of attack.