"Hein ten Horn" wrote in message
...
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 where did you apply the laws of physics?
You said, "It's just a matter of applying the laws of
physics." Then you did that for the single sine case. Where
is your physics calculation for the two sine case?
Where is the expression for 'f' as in your first
example? Put x(t) = 2 * cos(2pi 2 t) * sin(2pi 222 t)
in your calculations and tell me what you get
for 'f'.

And how do you get 222 Hz out of
cos(2pi 2 t) * sin(2pi 222 t)
Why don't you say it is 2 Hz? What is your
law of physics here? Always pick the bigger
number? Always pick the frequency of the
second term? Always pick the frequency of
the sine?
What is "the frequency" of
cos(2pi 410 t) * cos(2pi 400 t)


What is "the frequency" of
cos(2pi 200 t) + cos(2pi 210 t) + cos(2pi 1200 t) + cos(2pi 1207 t)



So my statements above, in which we have
a relatively slow varying amplitude (4 Hz),

How do you determine amplitude?
What's the math (or physics) to derive
amplitude?

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