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A question on Pendulum experiment
#17
(12-24-2020, 03:56 AM)solid Wrote: x = A sin(omega t)                                      # deviation angle
d sin(omega t) /dt= omega cos(omega t)
v = dx/dt = (A omega) cos(omega t)          # rotation speed
s = dA²omega²                                           # square standard deviation

'amplitude' calculated (dA² omega²)/omega/omega = dA² represents the standard deviation of the angle (for small harmonic oscillations)...
Cool i think.

This example is too complicated for a tutorial...

hmm, I think I'm not getting it.
I'm perfectly following up to this: v = dx/dt = (A omega) cos(omega t)          # rotation speed
but I do not understand this equation (or perhaps I'm misinterpreting the notation): s = dA²omega²  # square standard deviation
the standard deviation of: (A omega) cos(omega t) is, I think, A*omega/√2, so the square standard deviation would be A²omega²/2.  What does 'd' in this equation represent: s = dA²omega²  ?

Either way, the code at no point appears to be using the _square_ of standard deviation, so why is that stddev divided by (omega * omega) to get amplitude?
If the code was  ' stddev * √2 / omega ' then I would understand why the result is 'amplitude'.  (Although I think it would need to be stddev * √2 / (2*pi*frequency) since in the code frequency is in 1/s rather then in rad/s)
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Messages In This Thread
A question on Pendulum experiment - by jmnk - 11-30-2020, 08:39 AM
RE: A question on Pendulum experiment - by jmnk - 11-30-2020, 07:27 PM
RE: A question on Pendulum experiment - by jmnk - 11-30-2020, 07:50 PM
RE: A question on Pendulum experiment - by solid - 12-01-2020, 10:13 AM
RE: A question on Pendulum experiment - by solid - 12-01-2020, 10:18 PM
RE: A question on Pendulum experiment - by jmnk - 12-01-2020, 11:27 PM
RE: A question on Pendulum experiment - by jmnk - 12-02-2020, 12:41 PM
RE: A question on Pendulum experiment - by solid - 12-02-2020, 04:40 AM
RE: A question on Pendulum experiment - by jmnk - 12-02-2020, 04:49 AM
RE: A question on Pendulum experiment - by jmnk - 12-24-2020, 12:33 AM
RE: A question on Pendulum experiment - by solid - 12-24-2020, 03:56 AM
RE: A question on Pendulum experiment - by jmnk - 12-26-2020, 03:48 AM
RE: A question on Pendulum experiment - by jmnk - 01-04-2021, 07:36 PM
RE: A question on Pendulum experiment - by jmnk - 01-07-2021, 08:05 PM

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