The projections of the vector S change according to the harmonic law Sx = a1cos(wt + j1), Sy = a2cos(wt + j2), Sz = 0. Prove that the end of the vector S describes an elliptical trajectory in the xy plane. What is the equation of an ellipse? Show that this ellipse is inscribed in a rectangle with sides a1, a2 oriented along the x and y axes. Consider the special cases j1 = j2, j2 – j1 = n, j2 – j1 = ±. What is the motion of the end of the vector S along the ellipse in the latter case?

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