I had a question on doing a jump rope and thought I’d post the reply here.
I think nHair would be best for a jumping rope. A quick way is just create the rope curve… make selected curve dynamic and then just group the follicle… translate the follicle a little in the group and rotate the group node for the “pumping”. By default hairs created this way have point lock = base and tip so you don’t need any added constraints. Things like gravity and rate of pumping need to be correct. The higher the gravity the faster the pumping action required. The radius of pumping can start large then get smaller once it gets going( it is a type of resonance, and if you pump at the resonant frequency it takes very little energy to keep it going ). You may need higher stretch resistance and perhaps substeps if you have a lot of cvs on your curve( but 15 cvs should be plenty).
If both ends don’t pump in sync then you will need to add a transform constraint… point lock = base, then constraint the last 2 cvs.
In the simple attached example I did create hair with the options for 1 hair and 15 cvs on a plane. Then rotated the plane 90 deg, added a little translation then grouped. I moved the group up off the ground and animated its rotation to do the pumping. I sent point lock to both on the follicle and enabled ground collisions on the nucleus node. Because my curve was initially straight I set the rest length scale to 1.1 so it had some slack. I also increased the stretch resistance.