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




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