Resonance measurements free oscillations

Two unknowns require two measurements. For a free oscillator these measurements are the resonant frequency and the damping. For a forced oscillator the favored combination is the amplitude ratio and phase angle over a range of applied frequencies. This combination is not available for the evaluation of coatings because of the requirement that one surface be free. The two measurements described in the example below are damping and phase angle. 

The low-frequency motions of 5 MHz and 3 kHz lower the free energy of the folded and assembled structure of the elastic protein-based polymers. A coarse sense of the amount each mechanical resonance could be contributing to the stability of the structure of these elastic protein-based polymers is obtained from a plot of the logarithm of the frequency as a function of the entropy contribution of resonance frequency using the harmonic oscillator partition function. It is not expected that the harmonic oscillator would give an accurate measurement of the magnitude of the entropy contribution of such low-frequency motions. However, the use of the harmonic oscillator partition function provides a sense of direction and magnitude of the contribution of low-frequency motions to... 

QCM-D technique Kasemo and co-workers have developed an interesting technique that measures the resonance frequency f and the dissipation factor D, which is the inverse of the Q-factor, of the oscillation simultaneously by a ring down method. The quartz plate is excited every second with a frequency generator followed by switching off the source and recording the free decay of the quartz oscillation. The dissipation factor and resonance frequency are obtained from each cycle by a curve fit of an exponentially damped harmonic oscillator function (Figure 2C). 

ES, resonance electrostatic method FO, forced oscillation dynamic-mechanical analysis FV, free vibration TP, torsion pendulum TSC, thermally stimulated discharge current measurement D, dielectric VR, vibrating reed. 

The principle behind SFM is that the lateral or shear force between an oscillating probe tip and the sample increases as the distance decreases. The probe is usually mounted in a support such that several millimeters of the aperture end of the optical fiber extends beyond the clamping point. The probe thus forms a cantilever having one fixed and one free end. It is driven transversely at a so-called tip resonance , which indicates that the resonance is due to the cantilever rather than the support structure of the microscope, with an amphtude 5nm. Shear forces between the probe tip and sample surface damp the oscillation. The amplitude is measured and fed back to the sample height position so as to maintain constant oscillation amplitude and presumably constant tip-sample distance. The amplitude was measured, originally, with optical deflection methods. Recently, a number of electrical measurement schemes have been demonstrated that may prove to have a number of advantages in speed, sensitivity or ease-of-use [12]. In near-field single molecule experiments the bandwidth of the feedback is not an issue as scan rate is limited by... 

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