A　passive　timed　mass　damper　(TMD)　fabricated　using　the　Reid　damping,　referred　to　as　the　Reid-TMD,　is　proposed.　First,　the　characteristics　of　the　Reid　damping　model　are　introduced,　followed　by　the　presentation　of　a　passive　variable　friction　damper　to　achieve　this　model.　Next,　the　steady-state　response　of　single-degree-of-freedom　structures　with　the　Reid-TMD　under　a　harmonic　load　is　solved　by　the　harmonic　balance　method　(HBM),　together　with　an　error　analysis　of　the　results.　Subsequently,　the　optimization　and　control　effect　of　the　Reid-TMD　damping　system　are　analyzed　and　compared　with　the　traditional　viscous　damping　TMD.　The　results　show　that　under　the　action　of　a　harmonic　load　or　seismic　load,　the　vibration　suppression　effect　of　the　Reid-TMD　with　the　same　mass　ratio　is　essentially　equivalent　to　the　traditional　viscous　damping　TMD.　In　addition,　the　damping　control　effect　increases　with　the　increase　in　mass　ratio.　When　the　mass　ratio　is　less　than　0.05,　the　energy　dissipation　coefficient　is　less　than　0.5　and　the　frequency　ratio　is　less　than　0.95.　For　parameters　within　this　range,　the　steady-state　response　of　the　seismic　reduction　structure　with　the　Reid-TMD　is　solved　by　the　HBM.　If　the　parameters　of　the　Reid-TMD　are　outside　this　range,　the　error　of　the　HBM　becomes　large,　and　recourse　should　be　changed　to　general　numerical　methods.　The　optimum　parameters　of　the　Reid-TMD　are　determined　through　an　optimization　analysis　for　the　mass　ratio　in　the　range　of　0.005-0.1.　While　using　the　Reid-TMD　for　the　vibration　absorption　design,　the　optimum　parameters　can　be　acquired　directly　by　using　the　established　tables.　Because　the　passive　variable　friction　damper　has　good　durability　and　economy,　the　application　of　the　Reid-TMD　is　beneficial　to　shock　absorption　technology.