Resonant vibrations, which can cause machinery failure, occur when which of the following conditions happen?

Correct Answer: Option D — The frequency of an external vibration is the same as one of the natural frequencies of the machinery.

Resonance occurs when an external forcing frequency matches the natural frequency of a mechanical system. This synchronization causes a dramatic increase in vibration amplitude, potentially leading to rapid fatigue failure. Marine machinery must be designed and operated to avoid these critical speeds to maintain structural integrity and operational safety.