I had thought about writing an article on belaying and soft catches, but I don't think I could do better than this. 

http://homoclimbtastic.com/2012/05/20/better-belaying-the-soft-catch-aka-the-dynamic-catch/

Enjoy,

Marc

Very good article.  I must admit that I needed to read it as I had lost the fine art of jumping to soften a lead-on-bolts fall.  But then I almost exclusively lead-belay trad climbers ;-) 

I've never heard of this before, I always thought it was a technique for shitty pro/way to simulate a nice stretchy rope. I'm really not sure why this would soften the impact of any pendulums where a stretchy rope wouldn't.

A soft catch simply slows down the absorption of energy in a falls.

When executed properly the climber will have a significantly slower stop then if the belayer just held the belay device locked off and did nothing else.

Well typically pendulums, when expected, you have the rope already tensioned, i.e a tensioned traverse.

If you are on vertical or overhanging rock a fall with a pendulum is a really just a normal fall as far as the physics go. Obviously, there are other factors that come into play for the climbing in how they impact the rock.

When on a slab, the fall typically has much less force, as the climber is sliding or stepping back and the rope becomes taut. They are not falling that quickly so rope's dynamic capabilities are reasonable enough. If the climber is taking a serious lead fall on slab and has decided to run face first down the slap then they will be pointed in the wrong direction, assuming a tie-in in the front of the harness, and the forces considerably larger. Considering the forces involved and ledge/ground issues and I would think a soft catch would be reasonable.  Regarding the pendulum and decreasing of the pendulum by absorbing force with a soft catch, an easy way to prove it to yourself it to have a weight on a string and hold the weight with the rope taut. 

Scenario 1: let the weight go and note the span of the swing

Scenario 2: simulate a soft catch by lower the non-weight hand at the rate of the the weight, but a slowing rate. 

You should notice that the pendulum is dramatically less. 

My results:

Scenario 1: the weight swung about 80% of the height dropped.

Scenario 2: the weight swung about 20-30% of the height dropped.