Using the approximate expression of the Theodorsen function for the vertical motion of an airfoil given by \(z_{a}(t)=\mathrm{h} \cos (\mathrm{ks})\) where \(s=U t / b\), find the sectional lift coefficient change and plot it for \(k=0.1\) and for \(s\), with 

(i) Unsteady aerodynamics, 

(ii) Quasi unsteady aerodynamics,

(iii) Quasi steady aerodynamics.