The top comment of this post (Difficulties while trying to apply the Lagrangian approach to a problem with damping) mentions the importance of multiplying the standard lagrangian with $e^{\omega t}$ as the dissipation of energy requires an explicitly time-dependent Lagrangian.
I am using the Rayleigh Dissipation Function (RDF) instead of a generalised force (like the link above did) to account for the damping. Would I still need to include a time dependent lagrangian if I am using RFD? Or would a standard $L = T - V$ do.
