What happens to the phase when integrating from acceleration to velocity?

When integrating from acceleration to velocity, the phase experiences a shift of 90 degrees. This is rooted in the principles of Fourier analysis and the relationship between different types of vibrations.

Acceleration, being the second derivative of displacement with respect to time, is linked to velocity (the first derivative of displacement) by integration. Since integration of a function typically results in a phase shift, in the case of acceleration to velocity, this specific integration leads to a phase shift of 90 degrees.

To understand this better, consider that acceleration is represented as a cosine function in the frequency domain. Upon integrating, the resulting velocity becomes a sine function when expressed in the same context, leading to that characteristic 90-degree phase difference.

This concept is crucial, especially in vibration analysis, where understanding the relationships and shifts between different parameters can inform equipment diagnostics and predictive maintenance strategies. In practical applications, recognizing this phase shift can help in accurately interpreting vibration signals in various rotating machinery or structural analysis.