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 (15[1])process is halted by a “critical” phenomenon in which systems named for (-5[1])this process return to equilibrium immediately at zeta equals one. (-5[1])This process is described by the equation m (*) x double dot equals k x. (-5[1])External forces weaken this process through damping. Using (10[1])the small-angle approximation, a system named for this process can be used to model a pendulum. For 10 points, Hooke’s law describes “simple harmonic” systems performing what process? ■END■ (10[3])

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