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Differential EquationsMediumNonlinear Systems & Linearization

Nonlinear Systems & Linearization · Medium problem

A damped pendulum obeys θ′′+2θ′+5sin⁡θ=0\theta'' + 2\theta' + 5\sin\theta = 0. Write it as x=θx = \theta, y=θ′y = \theta'. The linearization at the origin has eigenvalues α±βi\alpha \pm \beta i with β>0\beta > 0. Find β\beta.