  The model we consider consists in a double pendulum set, where the pivot
points are free to shift along a horizontal line. Moreover, the two pendula are
coupled by means of a spring whose extremities connect two points of each
pendulum, at a fixed distance from the corresponding pivot. The mathematical
model is first written encompassing a large class of setting for the device
(different sizes, different physical properties, ...). In order to carry on the
problem of synchronization via analytical me\-thods, we focus on the
circumstance of identical pendula: in that case, some classical theorems
concerning the zeroes of polynomial equations are used in order to locate the
eigenvalues governing the process, so that the possibility of synchronization
of the device can be better understood.
