The motion of a pair of coupled oscillators may be described by using a method similar to that used in constructing a phase diagram for a single oscillator (Section 3.4). For coupled oscillators, the two position x1(t) and x2(t) may be represented by a point (the system point) in the two-dimensional configuration space x1-x2. As t increases, the locus of all such points defines a certain curve. The loci of the projection of the system points onto the x1- and x2-axes represent the motions of m1 and m2, respectively. In the general case, x1(t) and x2(t) are complicated functions, and so the curve is also complicated. But it is always possible to rotate the x1-x2 axes to a new set x1-x2 in such a way that the projection of the system point onto each of the new axes is simple harmonic. The projected motions along the new axes take places with the characteristic frequencies and correspond to the normal modes of the system. The new axes are called normal axes. Find the normal axes for the problem discussed in Section 12.2 and verify the preceding statements regarding the motion relative to this coordinate system.