In　the　dynamic　impact　response　analysis　of　the　structure，the　dynamic　amplification　factor(DAF)is　usually　used　to　simplify　the　calculation　of　the　dynamic　response　of　the　structure.　However，the　size　of　DAF　in　engineering　structures　is　still　controversial.　In　order　to　solve　this　problem，the　analytical　expression　of　DAF　of　multi-degree-of-freedom　system(MDOF)is　derived　in　this　paper，and　the　precondition　of　DAF　greater　than　2.0　is　analyzed.　The　accuracy　of　the　analytical　expression　is　verified　by　the　single-degree-of-freedom(SDOF)and　MDOF　example　models，and　the　reason　why　the　DAF　of　the　MDOF　is　greater　than　2.0　is　explained.　Finally，based　on　the　DAF　analytical　method　proposed　in　this　paper，the　DAF　distribution　law　of　beam　string　under　cable　breaking　impact　is　analyzed.　The　analysis　results　show　that　when　the　contribution　of　a　first-order　modal　shape　is　opposite　to　the　static　response，the　DAF　of　the　beam　string　may　be　greater　than　2.0.　Even　for　the　damping　system，the　DAF　of　the　beam　string　may　be　greater　than　2.0.　©　2025　Nanjing　University　of　Aeronautics　an　Astronautics.　All　rights　reserved.