The trajectory of a body with two simultaneous, mutually perpendicular oscillations is determined by x=asin(pomegat)""(1) y=bsin(qomegat+phi)""(2) where x and y are the projections of the body displacement on X and Y axes For simplicity, assume pomega=qomega=omega_(0). Then, the equation of trajectory will be y^(2)/b^(2)+x^(2)/a^(2)-(2xy)/(ab)cosphi=sin^(2)phi""(3) which is a general equation of ellipse. But if qomeganepomegaandpneq, then the graph of trajectory on the X-Y plane is either a closed curve, whose loop number is defined by the ratio n = p/q, or an open curve. Note that at the point where the curve reverses along the same trajectory, the velocities along the X-axis and Y-axis become equal to zero simultaneously. The body moving along the curve stops exactly at this moment at a certain point, say P, and then starts moving back, The closed curve for the motion of the body with the above two oscillations (1) and (2) with certain values of p, q and phi is given in the adjacent figure. The value of p/q is