Considering a design project here.

As an electrical engineer, I am well versed in the concept of the PLL - Phase Locked Loop.
What i am pondering is the idea of replacing the VCO with a mechanical oscillator that can have it's resonant frequency adjusted by a control signal. If the length of the pendulum could be dynamically adjustable via electro-mechanical means, it seems like it would not be hard to close the loop and achieve phase-lock with an external clock.

My idea is to have a linear array of pendulums that are constrained to a single axis of freedom, and have the ability to phase lock them to an external multi-phase clock.

The effect could be spectacular, as you could make them perform in beautiful patterns that could evolve from one to the next, by re-phasing the clocks and allowing the pendulums to come back into lock.

Any ideas on this one?

 

The PLL part is well understood except that the corner frequency of the loop filter is several orders of mag. lower than any PLL I have played with.

If I was building it, I would need to obtain the frequency vs control signal function, which means you will have to build the pendulum mechanism first...

I worked on a project like this in an earlier life. Seen the fountains at the Bellagio?

 

Some further musings.

What I am imagining is a system that has three distinct elements:

1) Amplitude control system- this part keeps the oscillation at a constant amplitude with closed loop feedback, pumping energy in to replace losses from friction, air resistance, etc.
I imagine using a moving magnet actuator to pump energy back in, and some type of angular displacement sensor to measure the swing amplitude. (and derive a clean phase feedback signal)

2) Frequency control system - the pendulum rod is mounted on a small hydraulic cylinder located on the pivot point, so the swinging length can be adjusted vertically to alter the natural frequency.
A tiny rotating hydraulic union couples fluid pressure to the swinging cylinder assembly, from an electric servo-actuated master cylinder controlling the fluid volume. The result should be a linear voltage to frequency transfer function. (alternately, the servo motor can be mounted on the swinging assembly, if I deal with those nasty moving wires.)

3) PLL system - this would be digital, implemented in a micro-controller to avoid analog drifts and leakage, problems that would plague a loop filter with such a long time constant.


A master clock would generate the polyphase clocks to drive the pendulums, another micro that has a bunch of counters that can be phase-shifted at will.
As long as the mechanical pendulum oscillators frequency range can accommodate the master clock frequency, things should work.

 

A Foucault Pendulum will always swing in a vertical plane and the apparent rotation is due to the earth revolving beneath it. However changing the length (and frequency or period) of a Foucault Pendulum does not change this plane.

Griffith Observatory in Los Angeles has a Foucault Pendulum and the drive mechanism is an ring shaped electromagnet.

The magnet is turned on and off by an optical sensor that's triggered when the suspension wire crosses the center and there's an adjustment for the current and also a timer for the duration of the current pulse. This technique provides very stabile resonance independent of the length.

 

My intention is to constrain the pendulum to a single axis of oscillation, by supporting it with a rigid rod and bearing supports, not by a flexible filament as with a true Foucault Pendulum.
I imagine the forces of precession would be absorbed by the bearings?

 

If you want to make an array oscillate in a predetermined pattern only, you should consider making the pendulum more immune to precession (the behavior of a true Foucault Pendulum) by using a smaller mass.

The motion can be restricted to only one plane of oscillation by pivoting the suspension rod on one half of a universal joint.

 

Smaller mass makes sense from many perspectives, as long as it's heavy enough to give a reasonable "Q" to the oscillator, too light, and it will be unstable.
The tuning mechanism needs to lift the mass, so a heavy pendulum would require a more robust mechanism.
Safety is also a concern, these things could whack you hard if you got in the way!