Here are my thoughts on the physics of the beater striking the head, rebound, etc. It seems to me that a few things happen in the course of a bass beater's travels throughout a note (utilizing rebound).
1. The foot pushes the pedal causing the spring to stretch (applying negative force back, against the foot) and the beater moves forward.
2. The beater strikes the head, the head moves the air through the drum while simultaneously absorbing part of the energy put into it from being struck, and also returns some energy repelling the beater.
3. The beater returns back to the position it began in.
At step 2 there are a couple of things that happen. A bass head is typically larger in diameter than others on your kit, and is slower to move a larger amount of air when struck. It ripples more when struck and absorbs more energy than smaller, more tightly-tuned heads on the rest of your drums. This is after all, why we have springs on our pedals, right?
The question is, after the head is struck, is is the rebound or the spring that first initiates the return of the beater, backwards. I would say it's the spring. The tension is always there and the spring is constantly pulling backward on the beater. Since the head absorbs much of the energy when struck, it makes sense that the spring will be the first thing to pull the beater back.
But, this could prove wrong if the spring has less tension than the amount of energy that is returned from striking the head. There are other variables too, like technique and what type of beater is being used.
I would think you'd have to consider your technique, how you tune, and what type of beater you're using to determine how much spring tension you need.
I'm not a physicist either, I'm just thinking out loud.
Well, as luck would have it, I am a physicist(well, a senior physics major, anyway). Sometimes people expect physics to spit out simple answers to complex problems, and it never does. I'll try to clear up what I can, though.
First of all, let's get our terms straight. Forces are pushes or pulls, and energy is the ability to do work. There are two basic kinds of energy, kinetic and potential. Kinetic is energy in motion, and potential is stored energy. Energy is essentially force times a distance, so they have different units(therefore, it makes little sense to compare them directly).
First, the spring. The spring equation is F=-kx(really only valid for small displacements), where F is the force, k is a number that depends only on the properties of the spring, and x is the distance the spring is pushed or pulled from equilibrium. What this says, then, is that the more you pull the spring, the harder the spring wants to pull back to its equilibrium length. So Zambizzi is right when he says the spring is constantly exerting a force on the pedal. Matt's also right that the spring stores energy, to the tune of kx^2. The kinetic energy of the pedal is transferred into the potential energy of the spring on the downstroke, and the reverse happens during the rebound phase. Note the nature of the force: it acts most strongly at the beginning and keeps acting as time goes on.
Now, the rebound off of the head. This is mostly the famous "every action has an equal and opposite reaction" law. As the beater impacts the drumhead, both will deform. The drumhead will deform inwards(towards the resonant head), and then snap back, pushing the beater away. The beater, similarly, will squish up and then push back out. I don't know of any equations that tell you how long this process takes; it's usually taken as essentially instantaneous. Keep in mind that this force is done acting as soon as the beater leaves the head.
I vote we ignore any effects of gravity, friction, quantum tunneling, etc. They're probably ridiculously small anyway.
I say all of this to allow you to try to draw your own conclusions. Here are my thoughts:
I see no particular reason for a delay in the action of the spring force. The spring itself is constantly pulling, and in fact is strongest when the beater is on the head. However, F=m*a, where m is mass and a is acceleration(This is the most important equation in mechanics). Therefore, this force will accelerate the beater as time goes on. The point is, the spring starts pulling instantly, but needs time to really accelerate the pedal.
The rebound, on the other hand, has completely transferred all of its energy to the pedal as soon as it leaves the head.
To be really rigorous, we'd need to measure the spring constant and measure the velocity of the beater as it strikes the head. We could then do some calculations and compare the actions of the two forces as time goes on. But if the two forces aren't too different(which they're probably not), we could suppose that the rebound has a faster response(completely done as soon as the beater's off the head), while the spring will be more important for everything that happens after that.
This seems to imply that the faster the double stroke, the more important the rebound is and the less important the spring is. If I may be so bold as to interpret Matt's techniques, however, I would say that the spring is important for getting the pedal away from the head and allowing one to return to a relaxed position. I'm sure someone else is more qualified to interpret the implications of this for technique, spring tension, etc, but it seems clear that both are necessary to be able to perform a variety of techniques.
Matt, I also want to thank you for the excellent DVD.
Hope this helps. Let me know if anything's unclear or if you see a mistake in my reasoning.