Resonance occurs when...

Resonance occurs when a forcing frequency coincides with a system’s natural frequency. In mechanical systems, every structure has natural frequencies at which it tends to vibrate when disturbed. When an external force is applied at a frequency that matches one of these natural frequencies, the system absorbs more energy from that force, causing the amplitude of the vibrations to increase significantly. This can lead to excessive vibrations, potentially damaging the equipment or system due to the amplified energy input.

The other options do not capture the essence of resonance. For instance, rotating looseness may cause vibrations, but it does not inherently involve the alignment of forcing and natural frequencies. Vibration levels increasing can occur for various reasons and doesn’t specifically indicate that resonance is happening. Similarly, variations in machine speed could lead to different vibrations or changes in forcing frequencies, but again, it does not automatically signify resonance unless those speeds align with natural frequencies. Therefore, the correlation between forcing and natural frequencies is crucial to defining resonance in vibration analysis.