Vibrating Inverted Pendulum

This Demonstration shows an inverted pendulum that vibrates sinusoidally at its base in the vertical direction at some frequency. The normalized vibration frequency is denoted by and the normalized vibration amplitude by . For some configurations of amplitude and frequency, the pendulum is relatively stable and stays inverted, while at others it starts to tumble. If or , you have a simple pendulum. The initial angle is measured from the vertical at time 0.