I sent the guy an email. I'm really not sure how else to get an answer to this "challenge."
E: OK, so I did email Henry Greenside about the problem, and he said that blowing through the straw on the bag was the correct answer. The problem was supposed to demonstrate the strength of resonance. In particular, he noted that the formula for the resonant frequency is independent of mass.
Of course, he was using the equation for simple harmonic motion, which ignores the damping that is highly relevant when dealing with a three hundred pound bag
and a drinking straw
This was the bulk of my response (sorry about the lack of LaTex, but it was an email):
We can model blowing through the straw as a sinusoidal driving force, blowing to push the bag and sucking to pull it. Ignoring phase for the moment, the steady-state solution for a driven oscillator is x(t) = F/(m Z w) sin(wt), where x is position, t is time, F is the driving amplitude, m is the mass of the bag, Z is the impedance, and w is the frequency of oscillation (which we will assume is the resonant frequency). As we can see, the amplitude is only F/(m Z w). Since this is inversely proportional to the bag's mass, it is difficult to imagine how one could overcome the damping. Given your value of w=0.25 Hz, and assuming that is also the undamped angular frequency w_0, and for simplicity assuming the damping coefficient is 0.5, we find Z = 0.25 Hz. Given also that the mass of the bag is 300 kg (ignoring the mass of the rope) and assuming we are trying to achieve an amplitude of 1m, we can solve for the required driving amplitude F = m Z w x = 19 N.
This is of course not an exact answer. If we let the damping coefficient vary from 0.1 to 0.9, we can get solutions from 5.3 N to 48 N, and the angular frequency is also a very approximate guess. However, even a force of 5 N is unobtainable by ordinary blowing. Consider trying to suspend a 10 lb weight by blowing on it from below. We are off by at least two orders of magnitude.
The case of blowing through a straw is actually worse. This is because it restricts the air flow, so we are not able to blow as quickly. You cannot fully exhale through a straw in two seconds.
I guess then the purpose of this email was to point out that damping due to air resistance makes simply blowing on the bag unfeasible. Another poster on the forum tried a different approach, comparing the driving force to the drag force and suggesting that even with a contact area of 0.125 cm^2 -- a huge opening to blow through -- we would need to blow air at 40 m/s, or 90 mph just to reach the bottle. That's a hurricane-force wind.
We also intutively know this. While powerful winds and mythical marching soldiers may be able to take down a bridge, a small subwoofer will not.