Module for the study of Oscillations and Resonance

Numerical Methods for O. D. E.  using Mathematica. (c) John H. Mathews, 2003

Background.

    We wish to study mechanical vibrations where the underlying D. E. is  

    .  

Example 1.  Investigate the beat frequency of an undamped forced oscillation. Consider the D. E.  

      with the I. C.  .  
  
Solve and plot the solution for  .

Example 2.  Investigate the steady periodic solution of the D. E.  

    .  

Example 3.  Investigate resonance of a damped forced oscillation.  Consider the D. E.  of the form

    .  

For illustration we shall investigate

    

The transient portion of the solution is

    

and is not influenced by the choice of   .

The steady state periodic portion of the solution is influenced by the choice of  .

Find and plot the steady state function for  

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