What a jerk

Induced vibrations for (2A) S-curve profile and (2B) trapezoidal profile

That an S-curve profile is smoother than a trapezoidal profile is evident from the above graphs. Why, however, do the Scurve profile result in less load oscillation? The answer to this has to do with the fact that for a given load, the higher the jerk, the greater the amount of unwanted vibration energy will be generated, and the broader the frequency spectrum of the vibration’s energy will be.

This means that the more rapid the change in acceleration, the more powerful the vibrations will be, and the larger the number of vibrational modes will be excited. This is shown in Figure 2. And because vibrational energy is absorbed in the system mechanics, it may cause an increase in settling time or reduced accuracy if the vibration frequency matches resonances in the mechanical and control system.