A mechanical rotating oscillator is used to demonstrate different bent tuning curves with basically the same system. A softening restoring force is realized by operating the oscillator as a gravitational pendulum. A hardening restoring force is realized by a spring acting on the oscillator. Tuning curves which are bent either to the right or to the left, as well as bistability and the jump effect, can be demonstrated. Furthermore, a doubly bent curve of amplitude versus frequency is shown to exist which gives rise to a doubly bent tuning curve and tristability. The experiments are a good introduction to unexpected phenomena related to nonlinear physics.