\fHint: Two examples are shown in Fig. 6.17 and are generated by the following equations and R code: x = a cos(kat) cos(wt), (6.166) y = a cos(kat) sin(wt), (6.167) where a = 3, w = 2, k = n for Fig. 6.17(a) and k = v2 for Fig. 6.17(b), and t goes from 0 to 30n.Calculate the velocity vectors for the point motion modeled in Figs. 6.17(a) and (b). Use hand calculation and analytic expressions