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