Controlling Hair dynamics in Blender can be very hard, since for the most part one has very little real control. Once things really start to move, they can quickly start to just fly out of control. About the most you can do is funny enough reduce or minimise the amount of movement, in order to keep it all together. The main settings that control that are the weight on the keys for each main hair particle strand and the Goal Strength.
This does mean that you do also need a fair number of particle keys (vertices or segments) on the hairs, both so that it has more points to interact with to calculate the simulation and so that you can control or limit how much it all moves down the strand. The Root is at value 1, along with maybe first one or two keys near the mesh surface at a high value (like 0.8-0.95), with maybe some lower values as it heads towards the tip, just so you actually get some movement.
You can then increase Goal Strength to help ‘keep it all together’ (values around 1-5 or maybe more can work), and then use Damping and Air Drag to quickly slow the movement down so that it stops.
Generally don’t be surprised if you need to use more then one hair particle system on an mesh, in order to have some sort of control, you may use half a dozen, also, long hair with dynamics, just isn’t something Blender does well, so a modification in design maybe needed.
Keep in mind, that the dynamics sim is only calculated on the main emitter hairs, there is no simulation or testing on any children hairs, but that doesn’t mean use a mass of emitter hairs either, as that will really slow things down and cause other problems.
Also makes sure Quality steps are at least around 10 or maybe a little more.