A simplified model of the classical Huygens' experiment on synchronization of pendulum clocks is examined. The model consists of two pendula coupled by an elastically supported rigid bar. The synchronized limit behaviour of the system, i.e. in-phase and anti-phase synchronization of the pendula, is studied as a function of the stiffness of the spring that supports the coupling bar. It is demonstrated that the stiffness has a large influence on the existence, stability, and oscillation frequency of the in-phase solution. The relationship between the obtained results and experimental results that have been reported in the literature, including Huygens' original observations, is stressed.