Concept explainers
Additional Mathematical Models
Damped Pendulum If we assume that a damping force acts in the direction opposite to the motion of a pendulum and with a magnitude directly proportional to the angular velocity dθ/dt, the displacement angle θ for the pendulum satisfies the nonlinear second-order differential equation
- (a) Write the second-order differential equation as a plane autonomous system. Find all critical points of the system.
- (b) Find a condition on m, l, and β that will make (0, 0) a stable spiral point.
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Differential Equations with Boundary-Value Problems (MindTap Course List)
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