9: Spring Models
- Page ID
- 24141
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Our final tool for mastering complexity is making spring models. The essential characteristics of an ideal spring, the transferable abstractions, are that it produces a restoring force proportional to the displacement from equilibrium and stores an energy proportional to the displacement squared. These seemingly specific requirements are met far more widely than we might expect. Spring models thereby connect chemical bonds (Section 9.1), xylophone notes (Section 9.2.3), gravitational radiation (Section 9.3.3), and the colors of the sky and sunsets (Section 9.4).
- 9.1: Bond springs
- A ubiquitous spring is the bond between the electron and proton in hydrogen—the bond that is our model for all chemical bonds. In Section 9.1.1, we’ll build a spring model of hydrogen, giving us a physical model for the Young’s modulus and for the speed of sound.
- 9.2: Energy Reasoning
- The previous analysis of sound propagation required estimating the spring forces. Often, however, the forces or their effects are harder to track than are the energies. Then, as you’ll see in the next examples, we track the energy and look for the energy signature of a spring: the quadratic dependence of energy on displacement.