My preferences are for the Y axis to be up.
Start off by drawing the curve (Create -> CV curve tool), snapping the cv's to the grid one unit at a time along the Z axis starting at 0,0 and placing them in -Z.
Next place a skeleton along the curve using Skeleton -> Joint Tool, starting at the point where you created your first cv. You need to have 2 bones and some bend in the middle joint to allow the end to move freely. Place an IK handle (Skeleton -> IK Handle Tool) on the skeleton from base of the skeleton to the other end.
Now select the skeleton and the curve and select Skin -> Bind Skin -> Smooth Bind. Pick the curve and turn it into a soft body Bodies -> Create Soft Bodies with "Duplicate, Make Soft Copy" selected and Hide Non-Soft Object and Make Non-Soft Goal Selected and weight set to 1.000. Select the new soft body, and create springs (Bodies -> Create Springs). The min/max setting are determined by where your cvs have been placed. In this case they were placed with 1 unit spacings, so I set min .1 and max 1.1.
Reselect the soft body, go to component selection mode with particle selecting on. Pick all of the soft body particles except the first and the last ones.
Open the Attribute Editor (Window -> Attribute Editor), go to the Per Particle (Array) Attributes section and with the right mouse button click in the gray box beside goalPP. Select Component Editor from the menu that appears. Change the goalPP to 0.00 for each of the selected particles then close the Component Editor and Attribute Editor.
Return to Object mode and select the soft body again. Create a gravity field (Fields -> Create Gravity). (If you play back the animation now the middle section of the curve should just fall straight down, the springs will eventually kick in but as long as the middle section falls you are in good shape)
Now is a good time to add the extrusion to your object. Create a circle and snap it to the first cv/particle of the soft body at the same end as the base of the skeleton and rotate it so that the circle is aligned in the image below. Select the circle then the soft body and perform an extrusion (Surfaces -> Extrude). Scale the circle to give the cord a nice diameter.
Create a nurbs plane which will act as the floor and our collision object and make it a collision object by selecting Particles -> Make Collide. Now click on Window -> Relationship Editors -> Dynamic Relations. In this editor you should select your soft body object (copy of Curve1) from the left side, then on the right side under Selection Modes check "Collisions" and select the floor object we created, nurbsPlaneShape1 or pPlane1 for a polygon floor.
You now have the basis of what we are trying to accomplish. From here tweaking is needed to get the cord to act the way you would like. A few channels affect this, the floor's Resilience and Friction and the Spring's Stiffness and Damping. For the example that I have created I set the Stiffness at 20, Damping at .5, Resilience at 0 and Friction at 0.2. You may need to increase the oversampling by using Solver -> Edit Oversampling to keep the Damping and Stiffness in the springs under control. The floor will need to be slightly lower than the rest position of the particles so that the chord won't drop through the floor on the first frame.
To test your settings, just animate the IK handle however you see fit.
QT MOVIE FILE (805K)
I created my cord in a straight line in order to space the springs evenly and to make as few of them as possible to speed up calculation time. You could create the cord in its curled position or move the IK handle end around until the cord animates to where you would like it and then select the soft body Solvers -> Initial State -> Set For Selected.
You might notice that half of the cord sinks below the floor plane. You can move the circle for the extrusion into a position so that the bottom edge of the extrusion is in the same place as the soft body curve.
Always extrude the circle on the softbody not the original curve and keep the construction history or the extrusion will not animate with the curve.