The equation of motion of a simple pendulum subject to viscous damping can be expressed as

\[\ddot{\theta}+c \dot{\theta}+\sin \theta=0\]

If the initial conditions are \(\theta(0)=\theta_{0}\) and \(\dot{\theta}(0)=0\), show that the origin in the phase-plane diagram represents (a) a stable focus for \(c>0\) and (b) an unstable focus for \(c<0\).