The　primary　goal　of　this　work　is　to　examine　the　dynamic　movement　and　chaos　of　a　governed　system　by　the　nonlinear　forced　Mathieu　equation　(NFME).　The　multiple-time-scales　approach　(MTSA)　is　applied　at　the　thirdorder　level　of　approximation　to　provide　the　approximate　solutions　of　this　equation.　Concurrently,　the　modulation　equations　(MEs)　are　created　and　the　resonance　case　is　investigated　according　to　the　solvability　restrictions.　Consequently,　the　solutions　are　verified　at　steady-state＇s　scenario.　The　criteria　of　Routh-Hurwitz　(CRH)　are　applied　to　investigate　and　appraise　the　stability/instability　zones　in　line　with　steady-state　solutions.　The　amplitudes　and　phases　throughout　a　designated　period　have　been　graphed　to　depict　the　motion　at　a　particular　instant.　Furthermore,　graphed　representations　of　the　acquired　results,　resonance　responses,　and　stability　regions　are　supplied　to　assess　the　impacts　of　different　applied　parameter　values　on　the　system＇s　conduct.　Three　first-order　equations　are　created　from　a　non-autonomous　second-order　differential　equation　(DE)　for　solving　computationally.　Utilizing　the　Runge-Kutta　algorithm,　various　motion　types　of　the　system　are　shown　according　to　a　bifurcation　diagram,　temporal　history,　Poincare　map,　Lyapunov　exponent　(LE),　and　phase　portrait.　The　outcomes　also　unequivocally　show　that　the　studied　model　possesses　rich　and　sophisticated　nonlinear　dynamic　phenomena,　including　periodic,　period-doubling,　period-quadrupling,　and　chaotic　vibrations.　Overall,　the　pendulum　model　described　by　the　NFME　has　diverse　applications　ranging　from　mechanical　engineering　and　structural　dynamics　to　seismology,　and　robotics.　It　offers　a　mathematical　foundation　for　comprehending　the　complex　dynamics　of　pendulum-based　systems　under　external　forcing　and　nonlinear　effects.