Wilberforce pendulum

A Wilberforce pendulum, invented by British physicist Lionel Robert Wilberforce around 1896, consists of a mass suspended by a long helical spring and free to turn on its vertical axis, twisting the spring. It is an example of a coupled mechanical oscillator, often used as a demonstration in physics education. The mass can both bob up and down on the spring, and rotate back and forth about its vertical axis with torsional vibrations. When correctly adjusted and set in motion, it exhibits a curious motion in which periods of purely rotational oscillation gradually alternate with periods of purely up and down oscillation. The energy stored in the device shifts slowly back and forth between the translational 'up and down' oscillation mode and the torsional 'clockwise and counterclockwise' oscillation mode, until the motion eventually dies away. A Wilberforce pendulum, invented by British physicist Lionel Robert Wilberforce around 1896, consists of a mass suspended by a long helical spring and free to turn on its vertical axis, twisting the spring. It is an example of a coupled mechanical oscillator, often used as a demonstration in physics education. The mass can both bob up and down on the spring, and rotate back and forth about its vertical axis with torsional vibrations. When correctly adjusted and set in motion, it exhibits a curious motion in which periods of purely rotational oscillation gradually alternate with periods of purely up and down oscillation. The energy stored in the device shifts slowly back and forth between the translational 'up and down' oscillation mode and the torsional 'clockwise and counterclockwise' oscillation mode, until the motion eventually dies away. Despite the name, in normal operation it does not swing back and forth as ordinary pendulums do. The mass usually has opposing pairs of radial 'arms' sticking out horizontally, threaded with small weights that can be screwed in or out to adjust the moment of inertia to 'tune' the torsional vibration period. The device's intriguing behavior is caused by a slight coupling between the two motions or degrees of freedom, due to the geometry of the spring. When the weight is moving up and down, each downward excursion of the spring causes it to unwind slightly, giving the weight a slight twist. When the weight moves up, it causes the spring to wind slightly tighter, giving the weight a slight twist in the other direction. So when the weight is moving up and down, each oscillation gives a slight alternating rotational torque to the weight. In other words, during each oscillation some of the energy in the translational mode leaks into the rotational mode. Slowly the up and down movement gets less, and the rotational movement gets greater, until the weight is just rotating and not bobbing.