Driven SHOs - The Resonance Response

References

Driven Simple Harmonic Oscillators

Resonance	Off- Resonance (source)
(source)	Click on image to enlarge (source)

Analysis of Driven SHOs

Equation of Motion

Important Analytic Tool - See Phasors, Vectors and Complex Notation

Use this relationship to encode force and displacement

Re-express Equation of Motion

Rearranging

or better

Resonance Resonance Curves - with damping

Modified Equation of Motion

Using Euler Theorem

where   

vs.                                     vs.                             (for  )                              (for  )