The　physics-informed　neural　network　(PINN)　is　an　effective　alternative　method　for　solving　differential　equations　that　do　not　require　grid　partitioning,　making　it　easy　to　implement.　In　this　study,　using　automatic　differentiation　techniques,　the　PINN　method　is　employed　to　solve　differential　equations　by　embedding　prior　physical　information,　such　as　boundary　and　initial　conditions,　into　the　loss　function.　The　differential　equation　solution　is　obtained　by　minimizing　the　loss　function.　The　PINN　method　is　trained　using　the　Adam　algorithm,　taking　the　differential　equations　of　motion　in　structural　dynamics　as　an　example.　The　time　sample　set　generated　by　the　Sobol　sequence　is　used　as　the　input,　while　the　displacement　is　considered　the　output.　The　initial　conditions　are　incorporated　into　the　loss　function　as　penalty　terms　using　automatic　differentiation　techniques.　The　effectiveness　of　the　proposed　method　is　validated　through　the　numerical　analysis　of　a　two-degree-of-freedom　system,　a　four-story　frame　structure,　and　a　cantilever　beam.　The　study　also　explores　the　impact　of　the　input　samples,　the　activation　functions,　the　weight　coefficients　of　the　loss　function,　and　the　width　and　depth　of　the　neural　network　on　the　PINN　predictions.　The　results　demonstrate　that　the　PINN　method　effectively　solves　the　differential　equations　of　motion　of　damped　systems.　It　is　a　general　approach　for　solving　differential　equations　of　motion.