Summary: The so-called penalty method in FE-calculation regularises the strong contact conditions by introducing contact stiffnesses and damping in order to reduce the mathematical effort. The problem, however, lies in an appropriate choice of the values of parameters for these artificially introduced springs and dampers. The principal problem of regularisation, however, can be studied for simple rigid body systems. As an example, two neighbouring physical pendulums with different natural frequencies are treated. During the motion sudden impacts and states of permanent contact interchange with states of separated motions of the two pendulums. The first step in the consideration comprises the calculation of a semi-analytical reference to classify the properties of the motion with regard to the main features of the non-linear system's response. The results are verified by experimental investigations in the next step. Finally, the system is regularised by the penalty method and integrated by Newmark's method. This procedure needs three unknown numbers, two regularisation parameters and a time step. Their correct choice depends on detailed information from the experimental results for each type of motion.