Hi, San Marcos. In a pure sense, there's no such thing as too much damping. Damping is simply reducing unwanted vibrations. There is no absolutely perfect damping material however, that eliminates vibrations 100%. Any vibration remaining will be influenced by the material and character that is doing the damping, and by the combination of materials in the vibrational path. Every vibrational environment is different also, so damping materials will interact sonically in different ways with different systems. With damping materials that are generally sonically neutral, efficient, and compatible with the vibrational environment they are dealing with, you will reach an optimal point. After that, you would be adding unnecessary damping and potentially subtracting from the optimal sonic results, especially if the damping materials are applied redundantly to address the same areas of vibration. Or if the same material is used virtually everywhere.
For example, placing Tenderfeet under a component usually provides vibration damping for improved performance. You can add a SuperSonic Stabilizer or two on top to supplement the job the Tenderfeet are doing. Damping the interconnects can reduce micro-vibrations infiltrating the component that would affect capacitors and other parts. Some rope caulk around the interior sides of the chassis and around circuit board mounts, etc. can be additionally beneficial. In this scenario, you don't have any redundancies, but complementary and supplementary damping.
If you were to go overboard with rope caulk, placing it everywhere in and around the component, a sonic "signature" of the rope caulk material would start to affect the sonic results, even though it is a very sonically neutral material. If you were to place compliant materials under the Tenderfeet you would alter the function of the Tenderfeet by unconstraining the vibration-absorbing material. In ways like these, overdamping is possible and very likely. It's not really "overdamping" however; you’re altering the vibrational environment instead of flatly reducing vibrations. Being caused by damping materials being applied inappropriately, you could call it overdamping.
Because micro-vibrational influence is inevitable, some components are designed by the manufacturer to counter inherent, internally generated vibrational anomalies, with their choice of resistor values and other design factors. By damping the internal parts, capacitors etc., you might inadvertently mess up the engineered design of the component. In most cases, however, moderately damping capacitors and other internal areas of a component will help bring out more of the engineered intent of the component.
Many damping materials, like rubber, Sorbothane, and others reduce vibrations but virtually always at the cost of some detrimental sonic trade-off because of the materials’ resonant and reverberant qualities. You want to avoid these kinds of materials as much as possible because “overdamping” will occur readily.
Another factor that is essential to understand yet difficult to explain is a phenomenon of system integration. Let’s say you have a component, for example a vacuum tube, that microphonics are affecting in a way that causes an over-emphasis of higher frequencies. You might compensate for that by using a damping material elsewhere in the system that attenuates those higher frequencies.
Suppose you then remedy the source of initial high-frequency emphasis by placing a damping instrument on the vacuum tube. The tube will subsequently provide a flatter frequency response but the attenuation that had been made elsewhere will now cause the overall audio result to be attenuated. Instead of leveling a peak, the attenuation will cause a dip. You then might assume that the damping instrument has “overdamped” when that is not at all the case, but is the consequence of a complementary aspect elsewhere.
So anyway, is there such a thing as too much damping? Yes and no. And yes.
Herbie's Audio Lab