Shocks are important, but DO NOT forget about imbalance if the oscilations "go away" above a certain speed. Yes, it's true that movable mechanisms have a natural frequency of oscillation, but I can assure you that unless there is some stimulus there will not be any oscillation. Frequency is not measured in miles per hour, it is measured in cycles per second,or some other time measurement, and amplitude or distance of travel.We are examining two separate issues here, and it is their sympathetic synchronization which gives rise to the effect.
If you put a wheel/tire assembly on a rotational balancer, it's own frequency will have nothing to do with the way its imbalance is detected. It is allowed to float in one plane, just as on the car, to detect how the centrifugal effect of its out of balance condition is affecting it through an imposed frequency in the machine.. If you now place it back on the vehicle, and it is perfectly balanced and perfectly round, and you drive it on a perfectly flat surface (bear with me here), there will be NO oscillation, good shock or NO SHOCK at all. There must be some stimulus, or input of energy,to begin the oscillation. Rotation alone will not provide that energy. In fact, you don't need any speed whatsoever to demenstrate the frequency of your suspension system.
Just remove all the fluid from your lever shock, or in the case of tube shocks, remove the shock altogether. Now, simply jounce the car up and down to begin the oscilations. If you have sensitive enough timing equipment you'll find that every up and down cycle takes precisely the same time, what ever the distance vertically traveled (the amplitude). You'll also see that the motion eventually does indeed stop. Without continued stimulus, or input of energy, the friction in the system, its friction against the air it must displace, and the effects of gravity itself will bring it to a halt in due time. Back to the tires./natural frequency thing.
The rotating mass that is the tire/wheel assembly must reach a critical rotational speed before its imbalance is sufficient to evercome the damping characteristics of the rest of the system, including the shocks, the bushings, and even the spring itself. True, a bad shock makes this easier, but until the rotational speed of the wheel reaches a point where its RPM coincides with the operational frequency of the suspension components, you'll experience no vibration. Once it does, Voila! you have the characteristic of an out of balance condition and you can feel it through the steering wheel. The average speed at which this happens for a wide variety of tire/wheel/suspension systems, because of the similarities of their designs, ranges from 52 to 60 MPH. But wait, there's more.
As you accellerate through this speed, and the rotational velocity of the tire/wheel assembly becomes significantly greater, it no longer is in sympathy with the natural frequency of the unsprung components of the suspension. Therefore, its influence diminishes. At some point it will even more or less perfectly oppose that frequency and reachieve a dynamic balance. Theoretically, if you double the speed at which the effect was first encountered it would return with a true vengence. I wouldn't advise it.
Of course, no matter how stiff the shocks are, if the out of balance weight is great enough, you will feel it. With a healthy shock the slight imbalance which virtually ALL our tire/wheel assemblies have is simply not noticed. Given a worn shock and a badly out of balance tire/wheel, you'll notice it big time. But, you must reach a critical speed for the mass which is out of balance to have sufficient influence upon the system.
So yes, you must have good shocks, but don't let that mask an out of balance condition, or that will wear out the new or rebuilt shocks much more quickly. It all has to work together. Remember. Shocks only do one thing. That is to damp oscillations. This they do by converting the energy which would continue those oscillations into heat, which is given off through the shock fluid and body. Energy doesn't get "absorbed". It can only be converted. Out of balance tires and wheels will cause the shock to work overtime and to heat up much more, causing it to eventually ruin its seals.
The driveshaft is another matter. It's speed is far greater, its diameter is far less, and the natural frequency of its support system is far higher. Even it, however, will tend to go in and out of phase. It just happens at a far greater rate, and the amplitude would continue to rise until something awful happened. I hope this all makes sense and assists you in maintaining your Healey. Cheers
Motorbill
From Lola to Land Rover, If it's British and has wheels, it's likely I've bloodied me knuckles thereupon