In this paper we study the dynamics of a system of two linearly couple
d, parametrically driven pendulums, subject to viscous dissipation. It
is a continuation of the previous paper (E.J. Banning and J.P. van de
r Weele (1995)), in which we treated the Hamiltonian case, The damping
has several important consequences, For instance, the driving amplitu
de now has to exceed a threshold value in order to excite non-trivial
motion in the system. Furthermore, dissipative systems (can) exhibit a
ttraction in phase space, making limit cycles, Arnol'd tongues and cha
otic attractors a distinct possibility. We discuss these features in d
etail. Another consequence of the dissipation is that it breaks the ti
me-reversal symmetry of the system. This means that several, formerly
distinct motions now fall within the same symmetry class and may for i
nstance annihilate each other in a saddle-node bifurcation, Implicatio
ns of this are encountered throughout the paper, and we shall pay spec
ial attention to its effect on the interaction between two of the norm
al modes of the system.