  We consider the mechanical motion of a system of six macroscopic pendula
which are connected with springs and arranged in a hexagonal geometry. When the
springs are pre-tensioned, the coupling between neighbouring pendula along the
longitudinal (L) and the transverse (T) directions are different: identifying
the motion along the L and T directions as a spin-like degree of freedom, we
theoretically and experimentally verify that the pre-tensioned springs result
in a tunable spin-orbit coupling. We elucidate the structure of such a
spin-orbit coupling in the extended two-dimensional honeycomb lattice, making
connections to physics of graphene. The experimental frequencies and the
oscillation patterns of the eigenmodes for the hexagonal ring of pendula are
extracted from a spectral analysis of the motion of the pendula in response to
an external excitation and are found to be in good agreement with our
theoretical predictions. We anticipate that extending this classical analogue
of quantum mechanical spin-orbit coupling to two-dimensional lattices will lead
to exciting new topological phenomena in classical mechanics.
