## Stress in an oscillating system

I'm a summer intern and I've been working on the design of a large-scale high frequency vibrating mechanism used for mixing. Although I have a nearly-complete design almost ready to be built, it represents a fairly large financial investement and I'm concerned about the stresses at work in the system.

If the system were static, calculating the maximum stress on each component could be done as simply the force divided by the smallest cross-sectional area. This calculation is usually not considered to be valid for a dynamic system, though, because the object experiencing a force will simply accelerate instead of experiencing stress and deforming. Certainly for a slow-moving system there is no reason for concern, but the mixer will oscillate with a frequency of 60 Hz! The acceleration experienced by one of the masses to achieve this frequency is 100 times larger than gravity, and the force is delivered through 16 springs- 8 above and 8 below (oscillation is only vertical.)

If it helps in explanation, you could consider a simple system with a mass attached to a single spring- How would you determine the maximum stress it experiences while oscillating? Is the fatigue life of the spring the dominating concern for this problem?