I thought some sums might be useful. Let’s suppose that the pendulum bob weighs 50 Newtons (~5 kg), pendulum length is 1 meter (seconds beating), and swing amplitude 1/30 radians (~2 degrees) (i.e. total arc is 4 degrees). It’s relatively easy to get a Q of 10,000 in a pendulum like this if it isn’t doing any work such as driving a count wheel or mechanical escapement.
The definition of Q is 2 x pi x (average stored energy) / (energy lost per cycle). For a high Q the average energy is ~ equal to the maximum when the bob is at its highest point. For our pendulum the bob lift at this highest point is (1 – cos(1/30)). Since cos(x) ~= 1 – x^2/2 + … for small x, then the max lift is
1 – (1 – 1/(30^2 x 2)) = 1/1800 m (~0.55 mm). The stored PE is then (50 N)/1800 = 1/36 joules. So the energy lost per cycle is:
2 x pi x (1/36)/10,000 = 17.45E-6 joules (17.45 microjoules). Assuming one impulse per cycle, the power input required is ~8.5 microwatts.
We need to deliver this energy by a short push on the bob, tangentially to its circular path, ideally near BDC. The total excursion of the bob is ~1/30 m, 33 mm, either side of BDC. Let’s suppose we apply a tangential force F over a 10 mm span – the energy imparted will be 0.01 m x F. Equating this to the energy required the force needed is 1.75E-3 N, about 0.18 grams-weight. Not a lot!
The scheme shown above applies a mainly vertical force downwards just before BDC. Because the pendulum isn’t quite vertical, there is a horizontal component of the force which can impulse the bob. Assume that the force is applied when the deflection is 1/60 radians (half amplitude). The horizontal component is F(vert) x sin(1/60) ~= F(vert)/60. Therefore we need to apply a vertical force to the pendulum bob 60 times greater than actually needed with this type of scheme. Not surprising that it may “twang”.
So in my view whilst this type of arrangement is easy to set up it is far from ideal. For example, it can only impulse the pendulum either early or late, not in the centre of the swing. It is not how Fedchenko arranged his impulsing – more of that when I find some pictures.