An alternating current (ac) magnetic field or spin current can reduce the switching field of a ferromagnet through resonance excitation of a large-angle precession of magnetization. The nonlinear magnetization dynamics of this switching scheme completely differ from the general ferromagnetic resonance phenomenon, which is linearly excited by a small ac magnetic field. To understand these dynamics, it is necessary to evaluate the effective potential barrier height for switching, ΔUeff. However, most previous studies have measured the consequent precession angle in the nonlinear dynamics by magneto-optical methods and/or by applying a magneto-resistive effect. Here, we applied the cooperative switching method, which evaluates the ΔUeff of the nonlinear dynamics under a sub-ns-wide magnetic field impulse, and observed a nontrivial reduction of ΔUeff in a submicron-wide NiFe strip. The strong reduction of ΔUeff under a negative magnetic field was caused by a saddle-node bifurcation in the nonlinear dynamics. In a micromagnetics simulation, we also confirmed that the magnetization is nonuniformly excited at the shallowest ΔUeff.