Ron Baker, Pluralitas! wrote:
"Hein ten Horn" wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:
Ron Baker, Pluralitas! wrote:
Hein ten Horn wrote:

As a matter of fact the resulting force (the resultant) is
fully determining the change of the velocity (vector) of
the element.
The resulting force on our element is changing at the
frequency of 222 Hz, so the matter is vibrating at the
one and only 222 Hz.

Your idea of frequency is informal and leaves out
essential aspects of how physical systems work.

Nonsense. Mechanical oscillations are fully determined by
forces acting on the vibrating mass. Both mass and resulting force
determine the frequency. It's just a matter of applying the laws of
physics.

You don't know the laws of physics or how to apply them.

I'm not understood. So, back to basics.
Take a simple harmonic oscillation of a mass m, then
x(t) = A*sin(2*pi*f*t)
v(t) = d(x(t))/dt = 2*pi*f*A*cos(2*pi*f*t)
a(t) = d(v(t))/dt = -(2*pi*f)^2*A*sin(2*pi*f*t)
hence
a(t) = -(2*pi*f)^2*x(t)

Only for a single sinusoid.

and, applying Newton's second law,
Fres(t) = -m*(2*pi*f)^2*x(t)
or
f = ( -Fres(t) / m / x(t) )^0.5 / (2pi).

Only for a single sinusoid.
What if x(t) = sin(2pi f1 t) + sin(2pi f2 t)

In the following passage I wrote "a relatively
slow varying amplitude", which relates to the
4 Hz beat in the case under discussion (f1 =
220 Hz and f2 = 224 Hz) where your
expression evaluates to
x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t),
indicating the matter is vibrating at 222 Hz.

So my statements above, in which we have
a relatively slow varying amplitude (4 Hz),
are fundamentally spoken valid.
Calling someone an idiot is a weak scientific argument.

Yes.
And so is "Nonsense." And so is your idea of
"the frequency".

Note the piquant difference: nonsense points
to content and we're not discussing idiots
(despite a passing by of some very strange
postings. ).

Hard words break no bones, yet deflate creditability.

gr, Hein