Eddy current displacement sensors measure the amplitude of vibration by detecting changes in the electromagnetic field caused by the movement of conductive materials, such as aluminum sheets. The sensor emits an alternating magnetic field, which induces eddy currents in the conductive material; the strength of these currents varies with the distance between the sensor and the sheet. As the sheet vibrates, the distance changes, allowing the sensor to measure the amplitude of the vibrations accurately. The time taken for the amplitude to halve is influenced by the magnetic flux density, which affects the sensor's sensitivity and response. Understanding these principles is crucial for effectively utilizing eddy current displacement sensors in vibration measurement applications.