  A simple and illustrative rheonomic system is explored in the Lagrangian
formalism. The difference between Jacobi's integral and energy is highlighted.
A sharp contrast with remarks found in the literature is pointed out. The
non-conservative system possess a Lagrangian not explicitly dependent on time
and consequently there is a Jacobi's integral. The Lagrange undetermined
multiplier method is used as a complement to obtain a few interesting
conclusions
