Relaxation　oscillations　are　pervasive　in　diverse　areas　of　natural　sciences　and　engineering,　and　exploring　the　dynamical　mechanisms　of　relaxation　oscillations　is　one　of　the　most　significant　issues.　Typical　relaxation　oscillations　can　be　observed　in　the　Duffing　system.　Recently,　amplitude　modulation　has　emerged　as　a　novel　control　mechanism　for　investigating　the　behavior　of　fast-slow　dynamics　in　systemic　tension　oscillations.　It　has　demonstrated　the　ability　to　prolong　the　quasi-static　slow　process　of　the　system　and　increase　the　number　of　bifurcation　points.　However,　the　exploration　of　the　mechanistic　aspects　of　amplitude　modulation　is　still　in　its　early　stages,　with　many　unreported　dynamical　mechanisms.　Among　these,　investigating　the　modes　of　relaxation　oscillations　induced　by　amplitude　modulation　is　one　of　the　most　important　issues.　Therefore,　this　manuscript　focuses　on　studying　the　effect　of　amplitude　modulation　on　relaxation　oscillations,　using　the　classical　forced　Duffing　system　as　a　representative　model.　Significantly,　we　report　an　intriguing　finding　for　the　first　time,　revealing　a　new　amplitude-modulated　mechanism　by　which　the　disappearance　of　relaxation　oscillations　can　be　induced.　By　employing　the　fast-slow　analysis,　we　have　examined　the　underlying　dynamical　mechanisms,　revealing　a　strong　correlation　with　the　modulation　index　of　amplitude　modulation.　Notably,　when　the　system　operates　under　low　amplitude　modulation,　an　extension　of　the　quasi-static　process　is　observed,　manifesting　as　a　prolonged　slow　process.　Conversely,　under　high　amplitude　modulation,　relaxation　oscillations　suddenly　disappear.　Our　results　serve　to　enrich　the　potential　mechanisms　of　amplitude　modulation,　and　our　analysis　provides　a　reference　for　investigating　the　dynamical　behavior　induced　by　amplitude　modulation　in　other　dynamical　systems.　©　2024　IOP　Publishing　Ltd.