Related Experiment Video
Updated: Aug 23, 2026

Real-Time DC-dynamic Biasing Method for Switching Time Improvement in Severely Underdamped Fringing-field Electrostatic MEMS Actuators
Published on: August 15, 2014
Hydrodynamic damping of a magnetically oscillated cantilever close to a surface
Christian Rankl1, Vasilli Pastushenko, Ferry Kienberger
1Institute for Biophysics, University of Linz, Altenbergerstr. 69, A-4040 Linz, Austria.
Abstract:
We studied the frequency response of a magnetically driven atomic force microscope (AFM) cantilever close to a sample surface in liquids. Amplitude-frequency (tuning) curves showed pronounced differences in dependence on the tip-sample separation (from 1 to 50 microm), with significant shifts of the resonance peak. A model was developed in which the cantilever was described in a full shape manner and the hydrodynamic forces acting on the cantilever were approximately calculated. The slight inclination of the cantilever to the surface (alpha approximately 15 degrees) leads to a force profile along the cantilever. Therefore, the mathematical problem can be strictly solved only numerically. For an approximate analytical solution, the hydrodynamic force profile was approximated by a constant force along the cantilever for large separations and by a point force acting on the tip of the cantilever for small separations. The theoretical results calculated within this model agreed well with the experimental data and allowed to determine the cantilever mass in liquid M*, the joint mass at the tip end m*t, and the coefficient of viscous interaction of the cantilever with free liquid, gamma(infinity).
More Related Videos
Related Concept Videos
Magnetic Damping
If, however, the bob is a slotted metal plate, the magnet produces a much smaller effect. When a slotted metal plate enters the field, an emf is induced by the change in flux; however, it is less effective because the slots limit the...
Types of Damping
Damped Oscillations
Although friction and other non-conservative...
Design Example: Underdamped Parallel RLC Circuit
Starting with a fixed...
Forced Oscillations
RLC Circuit as a Damped Oscillator
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...

