Compare two side-by-side springs, one linear and one non-linear. Adjust the magnitude of k3 so that the two masses start with the same initial force, and see if the period of the non-linear system is the same as the period of the linear system. Investigate how the period of the non-linear oscillation depends on the amplitude of the oscillation. Is mechanical energy conserved in your linear oscillator? Is mechanical energy conserved in your non-linear oscillator?