# ODELS10

The motion of a simple pendulum with a linear damping is governed by the equation $u''+vu'+\omega^2\sin u = 0\,$. where $v>0\,$.

In the $x-y\,$ phase plane for which $x=u\,$ and $\omega y=u'\,$, find all the critical points, classify them, and sketch the orbits near each critical point. Sketch the phase plane.

Notice: I missed a negative sign in the scanned homework: $\frac{y'}{\omega}=\frac{-v y}{\omega}-\omega^2\sin x\,$

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