This paper studies rare transitions between metastable states in Langevin systems that retain inertia. It shows that weak damping can change transition pathways and connections between states in ways that an overdamped approximation misses. The analysis rewrites the Freidlin-Wentzell action using time-reversed dynamics and adapts the string method to locate likely transition paths. The approach also treats velocity-dependent friction, where a conventional overdamped limit may not exist. Readers get both examples of when neglecting inertia changes the qualitative physics and computational tools for finding rare-event pathways in such systems.