Many thanks for that link, Duncan

The introductory text in the recent article contains a statement of analogy with which I was struggling:

Perhaps reading the  older paper will get me into the right frame of mind.

MichaelG..

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The problem is that the standing manoeuvre is only effective when the swing is already in motion … Presumably we are required to assume that  chaotic behaviour will suffice to get a pendulum away from its rest position.

… it probably will

… but it seems a convenient omission in the analogy

[ note particularly the final statement that I quoted ]

MichaelG.

The key is not to think of the bob motion but its acceleration.  Any vertical accelerations add to or subtract from the force of gravity.  Imagine that a vertical acceleration is applied just before BDC – this slightly increases the downward force and there is a small horizontal component of this which accelerates the bob slightly towards BDC and increases its energy. Similarly a deceleration after BDC accelerates the bob away from BDC.  Both tend to increase amplitude.

Another approach recognises that the tension in the rod at BDC is slightly greater because of the centripetal force on the bob.  A lift at BDC inserts energy as it works against this force which can only go into the bob’s kinetic energy.

Both approaches result in a fractional amplitude gain dA of

dA/A = h/L

where A is the amplitude, h the lift, and L the pendulum length. Obviously the pendulum has to be swinging initially for this to work.  Back in days before low noise microwave transistors were developed the bees knees for RF amplifiers in radio telescopes and suchlike was the parametric amplifier which used a varactor diode varying the resonant frequency of a cavity at twice the signal frequency.

The child on swing analogy is not very helpful I think as she can in effect create a lateral force by stick out her legs and drawing them in again.

This is all explained very well by Philip Woodward, HJ August 2005, or Chapter 3.4 of Woodward on Time.  He was inspired to think about the problem by the “clacker toy” which was the rage amongst kids 20 or so years ago.

There was an article in HJ September 1987 by Peter Wills about his “Dynadromic Free Pendulum” which worked on the same principle.  In the cathedral of Santiago de Compostela in Spain there hangs an incense burner called O Butafumeiro which swings through an 80* arc releasing copious amounts of smoke.  It can be raised and lowered on its suspending rope through a pulley system once set swinging by a gang of priests to “parametrically pump” its motion.

Duncan –

That basically my point. A person sitting or standing still on a swing will not make it move, and as you say simply imparts tension to the ropes.

Using a swing necessitates imparting a lateral force as well – and that is indeed how it is used. As soon as you lean forwards or backwards, you add a horizontal component to what had been at first a purely vertical force, neglecting any swining from the act of simply climbing on board. That component is from a combination of moving your centre of mass, and the reaction to your muscle movements – and those are usually, deliberately quite powerful.

This is where the analogy does not really explain the pendulum. What sets the pendulum moving in the first place?

A conventional escapement operates by one pallet being wedged sideways by an escape wheel tooth at each half-swing, to start the pendulum swinging, or balance-wheel oscillating, and to maintain the motion; but the effective radius is constant and it demands some energy input at each cycle.

The cathedral’s incense-burner will swing, of course, at a rate set by its depth below the pulley – and is large enough to keep swinging for a long time – but it still needs someone to start it swinging. If the priest did not do that but simply hauled it back up, it may well swing slightly, but from perturbations in letting go of it and hauling it up, especially if the pulley journals are themselves suspended instead of fixed rigidly to the ceiling.

So what does this electro-mechanical type of pendulum use? Does the bob move slightly to and from the centre-line in its vertical oscillation? If so then it will act rather as does the child on a swing, by the off-centre mass and its sideways movement creating a small horizontal force.

On 28 September 2025 at 15:28 duncan webster 1 Said:

No one is suggesting that you can start a pendulum by moving the bob up and down […]

Mmm … I guess it’s just a matter of semantics; but my reading of Ben Tubbing’s words was exactly that ^^^ suggestion

MichaelG.
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Quote:

To recall the essence: a parametric excitation pendulum is energised by varying the length of the pendulum

On 28 September 2025 at 16:32 Michael Gilligan Said:

On 28 September 2025 at 15:28 duncan webster 1 Said:

No one is suggesting that you can start a pendulum by moving the bob up and down […]

Mmm … I guess it’s just a matter of semantics; but my reading of Ben Tubbing’s words was exactly that ^^^ suggestion

MichaelG.
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Quote:

To recall the essence: a parametric excitation pendulum is energised by varying the length of the pendulum

Well, Mr Tubbing did say the child’s swing was an analogy, and meaning 2 of ‘analogy’ in my Compact OED is “a partial similarity”.

Top marks for spotting the disparity though – it went clean over my head.  As I got quite worried about it,  John’s explanation was most welcome.

A thought.  For lifting and dropping the bob to excite the pendulum it must already be swinging.   A real pendulum will be moving slightly even if it appears to be still.   But it’s not, the world is noisy.  In open air we have draughts.  In an enclosure, there will be thermal air currents.  Vacuums are not empty.  There are tidal effects, vibration due to traffic, and micro-seismic events.  And in practice, unless perfectly balanced, the parametric lifting mechanism will swing the pendulum slightly when starting.  Once a well-suspended pendulum is moving, even a tiny displacement will be enough for parametric pumping to add energy.

If I jump off a 20 story building, the earth moves when I land.  Not much, but it does.  That I grab all the attention by going spectacularly splat on the pavement doesn’t mean the planet is totally immobile.  And if the earth moves, so does a pendulum riding on it.

Dave

You do have the same angular velocity as the ground when attached to the building. When you let go the situation changes. Assuming your forward velocity remains the same when you hit the deck you will be travelling faster forward than the ground. This is why satellites have to slow down to drop into a lower orbit.

Don’t apologise Duncan it gets quite non intuitive very quickly. I can only intermittently visualise how tilted gyros appear to shift their mass to the pivot point.