Official Answer
Answer
Resonant vibration occurs when the pump's operating frequency $f_{op}$ matches the natural frequency $f_n$ of the retaining ring. The natural frequency is $f_n = \frac{1}{2\pi} \sqrt{\frac{k}{m}}$. When $f_{op} = f_n$, the ring's amplitude of vibration increases, leading to 'fretting' of the groove and eventually 'walking' the ring out of the groove. This is particularly dangerous for 'light-duty' rings with low mass and low grip. The solution is to change the ring's mass or stiffness (by changing the material or the number of turns) to move $f_n$ away from the operating range, typically ensuring $f_n > 2 \times f_{op}$.
