What is the term for converting acceleration to velocity or velocity to displacement?

The term for converting acceleration to velocity or velocity to displacement is integration. Integration is a fundamental concept in calculus that involves calculating the area under a curve, which represents the accumulation of quantities.

In the context of motion, when you integrate acceleration with respect to time, you obtain velocity, as velocity is the integral of acceleration. Similarly, when you integrate velocity with respect to time, you obtain displacement. This process is crucial in vibration analysis and dynamics, as it helps in translating the rates of changes of motion (acceleration and velocity) into physical positions or distances (displacement), allowing for a deeper understanding of an object's motion over time.

The other terms listed—differentiation, normalization, and regression—do not serve the same function in this context. Differentiation involves calculating a function's rate of change, which relates to converting position to velocity or velocity to acceleration, instead of the opposite. Normalization pertains to adjusting values into a common scale, and regression refers to statistical methods used to determine relationships between variables, neither of which applies to the conversion of these motion quantities.