Resonance is an issue for springs used in a dynamic cyclic loading environment, where the compressive force varies between two values. For example, the valve springs used in a car engine are subject to dynamic loads.
By design intent, a spring is a static mechanism. However, a spring will no longer behave as a static mechanism if the frequency of operation approaches the spring's first resonant frequency. Worse, the force the spring exerts on its boundaries will tend to decrease, which could have disastrous implications for the spring assembly.
In light of this, a rule of thumb for spring design is to make sure the frequency of operation is 15 to 20 times less than the first resonant frequency of the spring in question.
Use this calculator to find the first resonant frequency of a compression spring when you know its spring constant and its mass. (The spring mass can be found by weighing the spring.)