Official Answer
Answer
Multiple fractures (fragmentation) usually indicate resonance or harmonic vibration. If the frequency of the external load matches the natural frequency ($f_n$) of the spring, the internal stresses can amplify until they exceed the ultimate tensile strength. The natural frequency is $f_n = \frac{1}{2} \sqrt{\frac{K}{m}}$, where $m$ is the mass. In high-speed machinery, 'surge' waves travel through the spring coils. If the spring is not properly damped or if the operating speed is too close to $f_n$, the resulting 'dynamic stress' can be 5-10 times the static stress. Solution: Increase the spring's stiffness $K$ to move $f_n$ out of the operating range or add mechanical damping.
