  The present paper addresses the swing equation with additional delayed
damping as an example for pendulum-like systems. In this context, it is proved
that recurring sub- and supercritical Hopf bifurcations occur if time delay is
increased. To this end, a general formula for the first Lyapunov coefficient in
second order systems with additional delayed damping and delay-free
nonlinearity is given. In so far the paper extends results about stability
switching of equilibria in linear time delay systems from Cooke and Grossman.
In addition to the analytical results, periodic solutions are numerically dealt
with. The numerical results demonstrate how a variety of qualitative behaviors
is generated in the simple swing equation by only introducing time delay in a
damping term.
