Constant amplitude

Oscillations describes this cyclic characteristic. There are three types of oscillations that can occur in a control loop. They are decreasing amplitude, constant amplitude, and increasing amplitude. Each is shown in Figure 10. 

Note that if an analysis time-instant t" is not an integer, it can be rounded to the nearest integer prior to the calculation of the instantaneous frequency, provided that the corrected value of R(u - 1) = / - t"A is used in Eq. (7.14). It is easy to show that for a constant-amplitude, constant-frequency sinusoid, the procedure above outputs a perfect time-modified sinusoid2 provided... 

Figure 5.14 The tapping mode. The oscillation of the cantilever is dampened when the tip touches the sample surface at each cycle. The image is formed by keeping the oscillation amplitude constant. (Reproduced with permission from RC. Braga and D. Ricci (eds), Atomic Force Microscopy, Humana Press. 2004 Humana Press.)...

Instead of finding the equations of transformation from the q s to the Q s by the consideration of the kinetic and potential energy functions, we shall make use of the equations of motion. In case that all of the amplitude constants Q are zero except one, QI say, then Q, will vary with the time in accordance with Equation 37-13, and, inasmuch as the q s are related to the Q s by the linear relation... 

The principle of the experiment is shown in Fig. 6.5. A small air bubble is formed at the tip of a capillary which is immersed in the solution. Via an electrodynamic excitation system and a membrane, a gas volume directly connected with the capillary is excited to harmonic oscillations. From the excitation voltage of the system in dependence on frequency, while keeping the bubble oscillation amplitude constant, the dilational elasticity and the exchange of matter can be calculated. The comparatively complex theory for data interpretation was described recently by Wantke et al. (1980, 1993). The method can be applied in a frequency interval from 5 Hz up to about 150 Hz. 

The final check of the Kramer relations was to decrease the sample thickness while keeping the strain amplitude constant. The sample volume was decreased proportionally. These results are presented in Figure 3. In Figure 3 the modulus values are reduced by the SE 30 modulus at the same frequency as measured on the RMS. 

Load control, constant amplitude, constant rate of stress, tension. Observations... 

The high lateral forces and concomitant drawbacks of contact mode are circumvented in intermittent contact (also called tapping) mode AFM (Fig. 6.5). This mode utilizes an oscillating tip-cantilever assembly and relies on a feedback from the amplitude (constant amplitude imaging). A typical cantilever for operation in air is much stiffer than a contact mode cantilever (10-100 N/m) and is excited to resonance or near resonance. The forced oscillator is damped upon interaction of the tip with the sample surface (Fig. 6.5b and c). If the cantilever spring constant or the amplitude is too low, the energy in the forced oscillator is not sufficient to overcome the adhesive interactions and the tip remains trapped in contact and is consequently dragged across the surface. 

Constant amplitude, constant frequency, stress controlled, sinusoidal waveform... 

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