  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.
