Additional dynamical possibilities arise when we consider nonplanar string vibrations. These vibrations are also easy to excite with the string apparatus described in section 3.2. When a nonmagnetic wire is used, out-of-plane motions are observed which are sometimes called ballooning or whirling motions. These nonplanar vibrations arise even when the excitation is only planar.
Indeed, ballooning motions are hard to avoid. Imagine scanning the forcing frequency of the string apparatus through a resonance. The response of the string increases as the resonance frequency is approached, and the following behavior is typically observed. Well below the resonance frequency, the string responds with a planar, periodic oscillation (Fig.\ 3.16(a)).
Figure 3.16: Planar periodic, elliptical (nonplanar) periodic, and precessing
(quasiperiodic) motions of a string.
As the forcing frequency is increased, the amplitude of the response also grows until the string ``pops out of the plane'' and begins to move in a nonplanar, elliptical, periodic pattern (Fig. 3.16(b)). That is, the string undergoes a bifurcation from a planar to a nonplanar oscillation. At a still higher frequency the elliptical periodic orbit becomes unstable and begins to precess, as illustrated in Figure 3.16(c).
We will present a more complete qualitative account of these whirling motions in section 3.7.2, which is based on the recent work of Johnson and Bajaj [19], Miles [20], and O'Reilly [21]. Now, though, we turn our attention to the whirling motion that occurs when no forcing is present.