We show that the treatment of pendulum movement, other than the linear approximation,may be an instructive experimentally based introduction to the physics of non-linear effects. Firstly the natural frequency of a gravitational pendulum is measured as function of its amplitude. Secondly forced oscillations of a gravitational pendulum are investigated experimentally without limiting amplitudes. By this arrangement new phenomena, the bistability and the jump-effect, can be observed. In the case of bistability the driven gravitational pendulum can oscillate in two different stable modes. Either it oscillates with a small amplitude and approximately in phase with the exciting torque or it oscillates with a larger amplitude and approximately anti-phase. The jump effect is the spontaneous transition from one mode of oscillation to the other. Both effects can be demonstrated and explained.