What is the outcome when acceleration is integrated to obtain velocity in terms of phase change?

When acceleration is integrated to obtain velocity, there is a 90-degree phase shift in the resulting waveform. This is a fundamental concept in the analysis of periodic signals, particularly in the context of vibration analysis.

Acceleration is the derivative of velocity with respect to time. When you integrate acceleration, you are effectively reversing the differentiation process. This operation introduces a phase shift because, in the context of sinusoidal functions, integration leads to a change in the waveform's phase. Specifically, when you integrate a sine wave (representative of acceleration), the result is a cosine wave (representative of velocity), which is mathematically equivalent to shifting the phase by 90 degrees.

Understanding this phase relationship is crucial in vibration analysis, as it allows engineers and technicians to accurately interpret the behavior of mechanical systems and diagnose any potential issues related to vibrations.