I just did some calculations the other day on this matter and I'm going to have to say that the inertial force of the cone was not at play. The cabinet walking was either the bottom feet vibrating due to panel flex or air pressure changes from the sound waves lifting the cabinet. Here are my calculations, feel free to correct me if I missed something:

I ran a simulation in Hornresp which suggests you're an order of magnitude out on the acceleration.

You've made the following (inaccurate) assumption:

For a 60Hz sine wave, you've said that the cone accelerates linearly from rest to Xmax in 1/60th of a second. This is false in two ways.

First up, the acceleration will vary a lot according to where in the cycle you are. Acceleration is inversely proportional to displacement.

Secondly, the cone needs to move from rest to Xmax to -(Xmax) to rest to complete one cycle, so you've only got 1/240th of a second to go from rest to Xmax.

It would appear that the discrepancy largely cancels out, this is just in the interest of doing things right.

Here's a nice trick.

First, I'll define some variables, where a "1" following a letter indicates that's the property of the cone, and "2" indicates that of the cabinet.

a=acceleration

d=peak amplitude

F=force

m=moving mass

f=frequency

Also, a=d*(2pi*f)^2 from

https://en.wikipedia.org/wiki/Simple_harmonic_motion, looking at the maximum acceleration (we're not interested in any other case, since maximum acceleration produces maximum force).

Since, for both the cabinet and the cone, f is equal, we can write:

a1/d1=a2/d2

Then, from Newton's 3rd, F1=F2, m1*a1=m2*a2, so a1=m2*a2/m1

With some substitution and re-arranging, we can derive:

m1*d1=m2*d2

ie, the mass of the cone multipled by its peak excursion is equal to the mass of the cabinet multiplied by its peak excursion.

So, d2=m1*d1/m2.

In your case, d2=0.0675mm. You can go the long way around and work it out as you did. I got the same result both ways.

For the case of my 15" driver (mass of cone and voicecoil=160g*) in a 20kg box and 10mm one-way travel...

d2=0.08mm.

* should have used Mms on the T/S sheet, but I only had Mmd to hand, which doesn't include the air load of the cone.

Hardly seems enough to make the cabinet move much. I did hear it jumping around, though, and I do know that putting something heavy on top stopped it. Perhaps there was another mechanism at work. For instance, the distance of the driver from the floor could've produced a turning moment on the cabinet.

Out of interest, there's been at least one study about feeling vibrations:

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC151682/Looks like we can detect vibrations with an amplitude of the order of 10 microns, so something approaching 1/10th of a mm would be quite obviously vibrating when touched, even if we're unlikely to see the cabinet moving.

Chris