I have a general interest in jet engines and am pretty new to the topic so I wanted to toss this question into the wind as I don't have any previous experience or knowledge to pull from and haven't really found a similarly posted question anywhere else.
In the small amount of reading that I've done when looking at the RPM ranges for the various compressors (LP,IP,HP) generally the LPC spins the slowest and the HPC usually spins the quickest and, if the engine has one, the IPC has an RPM range that falls between the two.
So my question is what sort of speeds or fluctuation in speeds for each shaft could we expect during takeoff/flight/landing? For example does the LPC fluctuate more or less than the HPC/IPC or do they remain fairly constant while in flight?