This　paper　examines　the　behavior　of　a　two-degrees-of-freedom　(2DOF)　kinematic　system　of　the　spring　pendulum　coupled　to　a　harvester.　The　harvester　is　the　electromagnetic　device　that　is　reliant　on　a　magnet＇s　oscillation　within　a　coil.　Using　the　Lagrangian,　the　governing　equations　of　motion　(GEOM)　are　generated.　The　multiple-time-scales　approach　(MTSA)　is　employed　to　provide　the　analytical　solutions　(AS)　for　these　equations　up　the　third-order　of　approximations.　To　ascertain　these　solutions,　we　juxtapose　them　with　numerical　ones.　The　modulation　equations　are　set　up,　and　the　principal　external　resonance　instances　are　investigated　concurrently　upon　the　solvability　constraints.　A　schematic　representation　of　the　dynamical　system＇s　behavior　is　provided　by　the　time　histories,　phase　portraits,　and　nonlinear　stability　analysis　of　the　modulation　equations.　Moreover,　the　time　histories　of　the　electromagnetic　harvester＇s　current,　power,　and　voltage　are　shown　to　illustrate　how　various　parameters　impact　the　generation　of　electrical　energy.　According　to　the　Routh-Hurwitz　stability　criteria　(RHSC),　stability/instability　regions　exist　wherein　the　behavior　of　the　examined　system　is　stable　over　a　large　range　of　applied　parameters.　In　addition,　stable/unstable　fixed　points　within　the　scenario　of　steady-state　are　distinguished.　This　work＇s　relevance　is　confined　to　the　practical　implementations　of　its　findings　in　daily　life,　including　energy　sources　for　the　industrial,　electronic　and　medical　devices.