The nonlinear oscillations and resonances of the spring pendulum are experimentally and theoretically investigated. A unified by electromagnetic induction method of excitation, dissipation and registration of nonlinear oscillations is proposed. Experimental results demonstrate typical nonlinear effects, such as nonisochronism and bistability of vibrations. A theoretical model of the oscillatory system, leading to the Duffing equation, is proposed, an analytical solution and numerical simulation results are given, which agree well with the experiment.