I am a bit confused on the meaning of "slope" and the first and second derivatives.
I have an inclinometer that measures its angular orientation with respect to pure vertical, and it is traveling on a small cart up a beam that is compressed. The shape of the compressed beam can be approximated as a half sine wave, somewhat like this, ")" in real life. Thus, the inclinometer outputs the slope in degrees along the beam.
To approximate this I can construct a sine wave ie:
distance vs amplitude: sin(x) from x 0 to pi.
then taking the derivative to get the slope: cos(x)
(slope in what units? unit-less? wouldn't that be radians?)
to get radians: arctan(cos(x))
and degrees: arctan(cos(x)*(180/pi))
This gives the slope along the simulated rail in degrees. My question is this:
I have about 1000 data points in excel that are the slope along the rail in degrees vs distance from the start. I want to numerically integrate this data to get a graph of the amplitude of the bow along the rail vs distance.
Should I convert my degree slope data to radians, then take the tangent of that to get the actual slope "m"? Then integrate that data? Or integrate the radian data? What would be the physical significance (units?) of both methods?
This is kind of confusing because distance -> velocity -> acceleration when you are with respect to time, but I am plotting amplitude (distance) vs distance along the rail.
Sorry if that was long winded,