The (nonlinear) pendulum satisfies the ordinary differential equation d2x dt2 + sin x =
Chapter 14, Problem 14.8.1(choose chapter or problem)
The (nonlinear) pendulum satisfies the ordinary differential equation d2x dt2 + sin x = 0, where x is the angle. Equilibrium solutions satisfy sin x0 = 0. The natural position is x0 = 0, and the inverted position is x0 = . Determine whether an equilibrium solution is stable or unstable by considering initial conditions near the equilibrium and approximating the differential equation there. [Hint: Since x is near x0, we use the Taylor series of sin x around x = x0.]
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