In　industrial　applications,　the　connection　between　motor　drives　and　load　devices　often　relies　on　elastic　couplings,　which　are　prone　to　inducing　mechanical　resonance　issues.　Achieving　high-performance　and　high-precision　servo　control　requires　addressing　the　critical　challenge　of　effectively　suppressing　vibrations　in　two-inertia　systems.　This　paper　proposes　a　novel　mechanical　resonance　suppression　strategy　based　on　a　dual　extended　state　observer　(ESO).　The　root　causes　of　vibration　are　analyzed,　followed　by　an　investigation　of　the　system＇s　transfer　function.　The　performance　of　traditional　Proportional-Integral　(PI)　control,　ESO　control,　and　the　proposed　method　is　compared　through　Bode　plot　analysis　to　elucidate　the　working　principle　of　the　proposed　approach.　Simulations　conducted　in　a　Simulink　environment　compare　the　performance　of　the　proposed　vibration　suppression　method　with　that　of　traditional　PI　control.　Finally,　experimental　results　are　presented　to　validate　the　findings.　The　results　demonstrate　that　the　proposed　method　effectively　suppresses　speed　vibrations.　©　2025　IEEE.