A question on Pendulum experiment

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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)...
i think.

This example is too complicated for a tutorial...