It is a strange concept. Slowing time to come to speed. Given that when one does not have a VFD he just applies power and the motor starts up at the maximum acceleration rate it can for a given load.
You may want to check the wiring coming to your VFD. The throbbing at full speed that you observed is strange. Perhaps your supply to the VFD is marginal and so the input voltage going into the VFD is not stable. Make sure you have large enough wire for the run from the breaker box, that the breaker is good, and that the connections are all sound. ... Just some thoughts. When a motor is underload and trying to start it takes a lot more current and so the motor terminal voltage (and in this case the input voltage to the VFD) drops.
I once had a 1HP compressor on a 15Amp 110V circuit. It would start up fine when there was no air in the tank (no load). However, when the tank was partly full so that the motor had to start under a load it would stall. After a few seconds of being stalled it would trip the breaker. I rewired it to 220V 20Amp and the problem was solved. However, it was a pain to run the wires that were needed.
Dave L.