- #1
dfx
- 60
- 1
Hi,
I'll get right away to the point. I'm determining damping coefficients from motion sensor traces of a damped oscillator. I have gone through the standard procedure of taking natural logs of the sine wave peaks and drawing graphs etc, however what puzzles me is that the SIGN of the damping coefficient changes depending on whether u use the upper or lower envelope?
From [tex] x = e^{-pt} x_0 Sin [/theta] t [/tex]
Then taking logs:
[tex] lnx = -pt + lnx_0 Sin [/theta] t [/tex]
I asked my teacher in a hurry and he said the bottom envelope would be a reflection so the sign on the amplitude changes... however this doesn't affect the value of the damping coefficient after taking logs.. just the value of the y-intercept! Can anyone explain, help, and show mathematically please? Any feedback appreciated... thanks very much. Cheers.
edit: The graph I plotted was of 'lnx' against 't' to determine the value of 'p' and then further equate 'p' to 'b/2m' where 'b' is the damping coefficient. The problem is that with the upper envelope the value of 'p' - the gradient - is negative, so when you equate p = b/2m you end up with a negative value for b!
I'll get right away to the point. I'm determining damping coefficients from motion sensor traces of a damped oscillator. I have gone through the standard procedure of taking natural logs of the sine wave peaks and drawing graphs etc, however what puzzles me is that the SIGN of the damping coefficient changes depending on whether u use the upper or lower envelope?
From [tex] x = e^{-pt} x_0 Sin [/theta] t [/tex]
Then taking logs:
[tex] lnx = -pt + lnx_0 Sin [/theta] t [/tex]
I asked my teacher in a hurry and he said the bottom envelope would be a reflection so the sign on the amplitude changes... however this doesn't affect the value of the damping coefficient after taking logs.. just the value of the y-intercept! Can anyone explain, help, and show mathematically please? Any feedback appreciated... thanks very much. Cheers.
edit: The graph I plotted was of 'lnx' against 't' to determine the value of 'p' and then further equate 'p' to 'b/2m' where 'b' is the damping coefficient. The problem is that with the upper envelope the value of 'p' - the gradient - is negative, so when you equate p = b/2m you end up with a negative value for b!
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