Differential Equations › Section C · Second order differential equations › Topic C.11
Mechanical vibrations
A mass bouncing on a spring brings together everything in this section: the three kinds of roots become three kinds of damping, and the nonhomogeneous methods explain beats, resonance and the steady response to a driving force.
In this topic
- Building the model
- Free, undamped motion
- Worked example: amplitude and phase
- Free, damped motion
- Worked example: three dampers
- Forced motion without damping: beats
- Resonance
- Forced motion with damping
- Worked example: driving at the natural frequency
- The electrical analogy
- Common mistakes to avoid
- Key takeaways
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