Round 6: Tossup 20

Besides an inverse square force, a potential governing this process is the only one for which all bound orbits are also closed by Bertrand’s theorem. A nonlinear system named for this process was discovered by Balthasar Van der Pol. This process is halted by a “critical” phenomenon in which systems named for this process return to equilibrium immediately at zeta equals one. This process is described by the equation m (*) x double dot equals k x. External forces weaken this process through damping. Using the small-angle (10[1])approximation, (10[1])a system named for this process can be used to model a pendulum. For 10 points, Hooke’s law describes “simple harmonic” systems performing (-5[1])what process? ■END■ (10[2])

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