You should complete Section 5.1.1 before attempting this assignment.

Page 210, do problems:

• 21 – 24

• 25    Note: The question could be stated: "What is the maximum displacement below the equilibrium position?"

• 27, 29(a,c), 31

Use Maple wherever possible to check your work. See the Maple tutorial Solving Differential Equations.

Use Maple to plot your solutions as shown in this previous assignment.

Study these examples and their graphs:

1. Example 2 — Overdamped Motion
   See its graph.

2. Example 3 — Critically Damped Motion
   See its graph.

3. Example 4 — Underdamped Motion
   See its graph.

Click here to see examples of underdamped motion in meteorology:

• a satellite view of orographic lifting ("mountain clouds")
• a video of a gravity wave on YouTube* (not to be confused with a gravitational wave)

By the way, atmospheric science (meteorology) is a field in which fluid mechanics, heat transfer, thermodynamics, mathematics (of course), and even chemistry are applied. Fluid mechanics, heat transfer, and thermodynamics are usually taught by mechanical engineering departments, so next time a mechanical engineering prof says that you don't need math, ask what they know about the basis of meteorology.

---

See an animation of underdamped oscillation created by Dr. Russell, formerly of Kettering University.

---

* Neither I nor Kettering University endorses YouTube.