  Usually, in mechanics, we obtain the trajectory of a particle in a given
force field by solving Newton's second law with chosen initial conditions. In
contrast, through our work here, we first demonstrate how one may analyse the
behaviour of a suitably defined family of trajectories of a given mechanical
system. Such an approach leads us to develop a mechanics analog following the
well-known Raychaudhuri equation largely studied in Riemannian geometry and
general relativity. The idea of geodesic focusing, which is more familiar to a
relativist, appears to be analogous to the meeting of trajectories of a
mechanical system within a finite time. Applying our general results to the
case of simple pendula, we obtain relevant quantitative consequences.
Thereafter, we set up and perform a straightforward experiment based on a
system with two pendula. The experimental results on this system are found to
tally well with our proposed theoretical model. In summary, the simple theory,
as well as the related experiment, provides us with a way to understand the
essence of a fairly involved concept in advanced physics from an elementary
standpoint.
