A stretched string that is harmonically forced in one plane may exhibit motion in a perpendicular plane. Previous studies (see Bajaj and Johnson (1992)) have shown that if only one mode is directly excited in the plane of the excitation, the steady-state motion in the perpendicular plane will contain large amplitude motion only in the same mode. In other words, large amplitude, non-planar oscillations may occur only for n:n (e.g., 1:1 or 2:2) coupling. In this paper, it is shown that this result is not true for situations in which the mean force applied to the string is non-zero. A bias force, in combination with harmonic excitation at the second resonant frequency leads to out-of-plane motion of the first mode of the string. This 2:1 resonance is predicted by first-order averaging and is also seen in simulations and experiments.

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