Pendulum with Rotating Pivot

This Demonstration shows a special case of the damped and driven double pendulum. The suspension point (pivot) of a pendulum of length L and bob mass m is attached to a crank of length R rotating at a constant angular speed Ω. The damping coefficient of the system is μ. To limit the number of parameters, we take L=1 and the starting position of the bob at (Subscript[θ, 0])=15 °. Then the equation of motion is L m θ''(t)+L μ θ'(t)+ m g sin(θ(t))+m R (Ω^2)sin(t Ω -θ(t))==0. The animation traces the movement of the pendulum bob.

THINGS TO TRY

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DETAILS

Choose a set of parameters with the sliders or the "randomize parameters" button and start the animation. Or run the animation to the end and press the "randomize parameters" button to discover a variety of bob trajectories.

See: Equations of Motion of Damped and Driven Pendula

RELATED LINKS

Contributed by: Erik Mahieu

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