Harmonic oscillator weakly damped

For a weakly perturbed, harmonic damped driven oscillator, the resonance is shifted on the frequency scale depending on the sign of the interaction forces (Fig. 1.13). The availability of analytical expressions facilitates the applications of the weakly perturbed harmonic oscillator models for AM-AFM. Such harmonic models may be useful to illustrate the concepts used in AM-AFM well enough however, in most practical imaging cases, they do not describe the experiments [15]. 

Large-amplitude oscillations of a drop subject to the third mode initial deformation exhibit signs of other harmonics. These higher modes can be obtained by decomposing the surface into its harmonics (if a free drop undergoes a small amplitude axisymmetric oscillation in a weak damping limit) as ... 

Up to now we have considered the response function for a system of damped harmonic oscillators. If we allow for anharmonic interactions between phonons, the response function will be modified. The theory of crystal dynamics in which anharmonic effects are weak gives the following expression for the response function [5.47]... 

Fig,15.4. Classical explanation of the Hanle effect. The atoms behave like damped harmonic oscillators. The orbits of the oscillating electron for weak, medium, and strong magnetic fields are shown from left to right in the figure. 

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