Using the Fourier Transform to Solve the Harmonic Oscillator and Back-Transforming

All the derivatives have been removed, and we can solve for the Fourier transformed as a function of the transformation variable (in this case, ω).

Build in some physical assumptions for mass-spring-dashpot systems.

Back-transform to find the solution.

Otherwise, the complete solution (i.e., the inhomogeneous plus the homogeneous parts) can be calculated by the DSolve function

Created by Wolfram Mathematica 6.0  (26 November 2007)