We've recently become interested in head shake on bikes, also known as shimmy or speed wobble or death wobble. It is of interest because cargo bikes favour less trail to avoid heavy steering when loaded, but this leaves them vulnerable to shimmy at higher speeds.
High speeds are not an everyday occurrence with cargo bikes; but when travelling down hill, faster than normal speeds can produce unwanted head shaking.
This phenomena is sometimes referred to as a resonance, because of it's similarity to a resonant condition and the occurrence of oscillations. However it is subtly different.
Briefly: Resonance refers to a system which has a known resonant frequency. A spring for example can be compressed, then released and it will oscillate at its natural resonant frequency.
In the case of head shake the problem is actually known as a Bifurcation. This is the mathematical name for a system which shakes or flutters. There are many types of bifurcations, and they explain all sorts of phenomena in nature such as aeroplane wing flutter, stability of bicycles, shopping trolley wheel shake and even the famous Tacoma Narrows bridge failure. A bifurcation can be described as "the dynamic instability of an elastic structure, where there is feeding between the deformation of the structure and the force being applied." The interaction between the structure and external forces can lead to a rapid increase in the amplitude of the oscillations and can quickly lead to a catastrophe.
[It is interesting to note that all aircraft have to pass a high speed dive test to check for flutter from the wings, tail or anywhere in the structure. This is the most dangerous step in all of the air worthiness testing]. https://www.youtube.com/watch?v=ImSuZjvkATw
Back in the bicycle world, what does this mean and how can it be avoided?
Known fixes include making the frame torsionally stiffer and the wheels laterally stiffer, the frame lighter or by adding a steering damper; even inflating the tyres more may help.
If it happens when riding you can stand on the pedals which places your weight lower down on the frame, or clamp the crossbar with your knees to add stiffness. Holding the handlebars lightly to dampen the system should help, rather than holding tightly and connecting yourself to the wobbling mass.
With cargo bikes - many of these options are limited. Increasing frame stiffness of these larger bikes can add excessive weight and likewise, making the frame light can leave it weak.
The ideal fix however (as any motorcyclist will tell you) is the fitting of a steering damper. This categorically removes the possibility of head shake at any speed, on any frame, carrying any load; because the added friction in the steering system limits steering movement to a speed below that which bifurcations can occur.
It is the responsibility of a bicycle designer to ensure that head shimmy is reduced to a controllable level and that if it does occur, it is at a speed outside of reasonable riding conditions. Rodford Box bikes come with lots of thinking about this phenomenon from the drawing board.