Usually, in mechanics, we obtain the trajectory of a particlein a given force field by solving Newton’s second law withchosen initial conditions. In contrast, through our work here,we first demonstrate how one may analyze the behaviour of asuitably defined family of trajectories of a given mechanicalsystem. Such an approach leads us to develop a mechanicsanalogue following the well-known Raychaudhuri equationlargely studied in Riemannian geometry and general relativity.The idea of geodesic focusing, which is more familiar toa relativist, appears to be analogous to the meeting of trajectoriesof a mechanical system within a finite time. Applyingour general results to the case of simple pendula, weobtain relevant quantitative consequences. Thereafter, weset up and perform a straightforward experiment based ona system with two pendula. The experimental results of thissystem are found to tally well with our proposed theoreticalmodel. In summary, the simple theory and the related experimentprovide us with a way to understand the essence of afairly involved concept in advanced physics from an elementarystandpoint.