Chapter 7. Free Vibrations

  1. Prof. Dror Sarid

Published Online: 16 FEB 2007

DOI: 10.1002/9783527610068.ch7

Exploring Scanning Probe Microscopy with MATHEMATICA, Second Edition

Exploring Scanning Probe Microscopy with MATHEMATICA, Second Edition

How to Cite

Sarid, D. (2006) Free Vibrations, in Exploring Scanning Probe Microscopy with MATHEMATICA, Second Edition, Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, Germany. doi: 10.1002/9783527610068.ch7

Author Information

  1. College of Optical Science, University of Arizona, Tucson, Arizona 85721, USA

Publication History

  1. Published Online: 16 FEB 2007
  2. Published Print: 15 DEC 2006

ISBN Information

Print ISBN: 9783527406173

Online ISBN: 9783527610068

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Keywords:

  • scanning probe microscopy;
  • MATHEMATICA;
  • free vibrations;
  • equation of motion;
  • analytical solution;
  • numerical solutions

Summary

This chapter contains sections titled:

  • Introduction

  • Equation of Motion

  • Analytical Solution

    • Equation of Motion

    • Steady-State Regime

    • Bimorph–Cantilever Phase

    • Q-Dependent Resonance Frequency

    • Frequency-Dependent Amplitude

    • Frequency at the Steepest Slope

    • Average Power

  • Numerical Solutions

    • Equation of Motion

    • Transient Regime

    • Bimorph–Cantilever Phase Diagram

    • Displacement–Velocity Phase Diagram

  • Exercises for Chapter 7

  • References