Force-induced resonance , nonlinear

Figure 6 presents the force gain of the suspension in the vertical direction for each of the three dampers when subjected to single harmonic force inputs of different peak amplitude level. The results obtained with the linear damper indicate that the entire model is basically linear. The geometrical nonlinearities were found to be small for the suspension rotations induced ( 3 degrees). The situation changes somewhat in the case of the bilinear damper, where nonlinear effects are now visible in the immediate neighborhood of the main suspension resonance (2.95 Hz). 

The detailed studies show that the saturation of the common level, as discussed above, is not the only coupling mechanism. The interaction of the atom with a light wave generates an induced dipole moment which is at small intensities proportional to the field amplitude. At higher intensities the nonlinear terms in the induced polarization become important. If two waves with frequencies and simultaneously act in resonance with the atom, these nonlinear terms produce sum and difference frequencies For two transitions which share a common level the difference frequency - W2 is in resonance with the atomic transition b c (2 2 - 3 2) and will therefore modulate the atomic polarization at the frequency - 0)2 The phenomenon can be regarded as a resonant Raman process where the 0.63 ym transition generates the Stokes line at X = 1.15 ym and both waves force the electronic polarization to oscillate at the difference frequency (see Sect.9.4). 

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