The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $beta$ and the periodic solution, and a conclusion that the critical value of $beta$ is a fixed one in the over damping situation. These results are of practical significance in the study of charge-density waves in physics.
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