Vibration Analysis

Every mechanical system has its own natural frequency — when an external excitation (motor vibration, rotating imbalance, road/ground motion) approaches this frequency, the system goes into resonance and the vibration amplitude can reach dangerous levels. The 1940 collapse of the Tacoma Narrows Bridge is the best-known example of resonance’s destructive effect.

This tool calculates the fundamental dynamic properties of a single-degree-of-freedom (mass-spring-damper) system: natural frequency (ωn), critical damping, and damping ratio (ζ). The damping ratio determines the system’s behavior:

• ζ = 0: Undamped — oscillates indefinitely
• 0 < ζ < 1: Underdamped — oscillates with decreasing amplitude (most real systems)
• ζ = 1: Critically damped — returns to equilibrium fastest without oscillating
• ζ > 1: Overdamped — returns to equilibrium slowly without oscillating

Design rule: keeping the operating (excitation) frequency at least 20–30% away from the natural frequency practically eliminates resonance risk. Solutions such as shape-memory-alloy (SMA) based passive dampers are used to increase the damping ratio and reduce vibration amplitude.